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Paul Binding

photograph of Paul Binding

Job Title:

  • Professor
  • University Professor

Phone:

  • +1 (403) 220-6328

Office:

  • MS 518

Email:

Degrees:

Research Interests:

  • Eigenvalue problems of an unusual type, e.g. containing several parameters, or of indefinite type; sample problems include oscillation of eigenfunctions, variational principles and asymptotics.
  • Differential equations of an unusual type, e.g. containing discontinuous or set-valued right hand sides, with application to control theory
  • Minimum energy problems for musculoskeletal models.

Teaching:

Past Courses:

  • AMAT425 - INTRODUCTION TO OPTIMIZATION
  • AMAT621 - Research Seminar
  • AMAT621A - Research Seminar
  • AMAT621B - Research Seminar
Representative Publications:
Journal Paper
Binding, Paul and {\'C}urgus, Branko . "A counterexample in {S}turm-{L}iouville completeness theory" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 134.2 (2004): 244-248
Binding, Paul, Browne, Patrick and Watson, Bruce. "Equivalence of inverse {S}turm-{L}iouville problems with boundary conditions rationally dependent on the eigenparameter" J. Math. Anal. Appl. 291.1 (2004): 246-261
Binding, Paul and Ko{\v{s}}ir, Toma . "Root vectors for geometrically simple two-parameter eigenvalues" Transactions of the American Mathematical Society 356.5 (2004): 1705-1726 (electronic)
Binding, Paul and Volkmer, Hans . "Right semidefinite eigenvalue problems" Proceedings of the Edinburgh Mathematical Society. Series II 46.3 (2003): 561-573
Binding, Paul, Browne, Patrick and Watson, Bruce. "Decomposition of spectral asymptotics for {S}turm-{L}iouville equations with a turning point" Advances in Differential Equations 8.4 (2003): 491-511
Binding, Paul. "A hierarchy of {S}turm-{L}iouville problems" Mathematical Methods in the Applied Sciences 26.4 (2003): 349-357
Binding, Paul and Dr{\'a}bek, P. . "Sturm-{L}iouville theory for the {$p$}-{L}aplacian" Studia Scientiarum Mathematicarum Hungarica. A Quarterly of the Hungarian Academy of Sciences 40.4 (2003): 375-396
Binding, Paul, Browne, Patrick and Watson, Bruce. "Sturm-{L}iouville problems with boundary conditions rationally dependent on the eigenparameter. {II}" Journal of Computational and Applied Mathematics 148.1 (2002): 147-168
Binding, Paul and {\'C}urgus, Branko . "Form domains and eigenfunction expansions for differential equations with eigenparameter dependent boundary conditions" Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 54.6 (2002): 1142-1164
Binding, Paul, Browne, Patrick and Watson, Bruce. "Sturm-{L}iouville problems with boundary conditions rationally dependent on the eigenparameter. {I}" Proceedings of the Edinburgh Mathematical Society. Series II 45.3 (2002): 631-645
Binding, Paul, Browne, Patrick and Watson, Bruce. "Spectral asymptotics for {S}turm-{L}iouville equations with indefinite weight" Transactions of the American Mathematical Society 354.10 (2002): 4043-4065 (electronic)
Binding, Paul, Browne, Patrick and Watson, Bruce. "Inverse spectral problems for left-definite {S}turm-{L}iouville equations with indefinite weight" J. Math. Anal. Appl. 271.2 (2002): 383-408
Bhattacharyya, T. , Binding, Paul and Seddighi, K. . "Multiparameter {S}turm-{L}iouville problems with eigenparameter dependent boundary conditions" J. Math. Anal. Appl. 264.2 (2001): 560-576
Binding, Paul and Volkmer, H. . "Oscillation theory for {S}turm-{L}iouville problems with indefinite coefficients" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 131.5 (2001): 989-1002
Binding, Paul, Browne, Patrick and Watson, Bruce. "Transformations between {S}turm-{L}iouville problems with eigenvalue dependent and independent boundary conditions" The Bulletin of the London Mathematical Society 33.6 (2001): 749-757
Binding, Paul, Hryniv, R., Langer, H. and Najman, B. . "Elliptic eigenvalue problems with eigenparameter dependent boundary conditions" J. Differential Equations 174.1 (2001): 30-54
Binding, Paul and Volkmer, H. . "Existence and asymptotics of eigenvalues of indefinite systems of {S}turm-{L}iouville and {D}irac type" J. Differential Equations 172.1 (2001): 116-133
Bhattacharya, T. , Binding, Paul and Seddighi, K. . "Two-parameter right definite {S}turm-{L}iouville problems with eigenparameter-dependent boundary conditions" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 131.1 (2001): 45-58
Binding, Paul, Eschw{\'e}, David and Langer, Heinz . "Variational principles for real eigenvalues of self-adjoint operator pencils" Integral Equations and Operator Theory 38.2 (2000): 190-206
Binding, Paul and Najman, Branko . "The minimal index of a self-adjoint pencil" Glasnik Matemati\v cki. Serija III 35(55).1 (2000): 25-44
Binding, Paul, Browne, Patrick and Watson, Bruce. "Inverse spectral problems for {S}turm-{L}iouville equations with eigenparameter dependent boundary conditions" Journal of the London Mathematical Society. Second Series 62.1 (2000): 161-182
Binding, Paul and Hryniv, R.. "Relative boundedness and relative compactness for linear operators in {B}anach spaces" Proc. Amer. Math. Soc. 128.8 (2000): 2287-2290 (electronic)
Binding, Paul, Browne, Patrick and Watson, Bruce. "Spectral problems for non-linear {S}turm-{L}iouville equations with eigenparameter dependent boundary conditions" Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 52.2 (2000): 248-264
Binding, Paul and Browne, Patrick. "Sturm-{L}iouville problems with non-separated eigenvalue dependent boundary conditions" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 130.2 (2000): 239-247
Binding, Paul, Dr{\'a}bek, Pavel and Huang, Yin . "Existence of multiple solutions of critical quasilinear elliptic {N}eumann problems" Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods 42.4, Ser. A: Theory Methods (2000): 613-629
Binding, Paul, Dr{\'a}bek, Pavel and Huang, Yin . "Positive solutions of critical quasilinear elliptic equations in {${\bf R}\sp N$}" Math. Bohem. 124.2-3 (1999): 149-166
Binding, Paul, Najman, Branko and Ye, Qiang . "A variational principle for eigenvalues of pencils of {H}ermitian matrices" Integral Equations and Operator Theory 35.4 (1999): 398-422
Binding, Paul and Ko{\v{s}}ir, Toma . "Multiparameter spectral theory" Dru\v stvo Matematikov, Fizikov in Astronomov Slovenije. Obzornik za Matematiko in Fiziko 46.2 (1999): 42-44
Binding, Paul and Browne, Patrick. "Form domains for sectorial operators related to generalized {S}turm-{L}iouville problems" The Quarterly Journal of Mathematics. Oxford. Second Series 50.198 (1999): 155-178
Binding, Paul and Volkmer, Hans . "A spectrum determined by eigencurves" Mathematische Nachrichten 202 (1999): 5-15
Binding, Paul and Browne, Patrick. "Left definite {S}turm-{L}iouville problems with eigenparameter dependent boundary conditions" Differential Integral Equations 12.2 (1999): 167-182
Biles, Daniel C. and Binding, Paul. "Subfunctions and cone conditions for initial value problems" The Canadian Applied Mathematics Quarterly 5.4 (1997): 321-329
Binding, Paul and Browne, Patrick. "Oscillation theory for indefinite {S}turm-{L}iouville problems with eigenparameter-dependent boundary conditions" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 127.6 (1997): 1123-1136
Binding, Paul, Dr{\'a}bek, P. and Huang, Y. X. "The range of the {$p$}-{L}aplacian" Applied Mathematics Letters. An International Journal of Rapid Publication 10.6 (1997): 77-82
Binding, Paul, Browne, Patrick and Seddighi, K. . "Two parameter asymptotic spectra in the uniformly elliptic case" Results in Mathematics. Resultate der Mathematik 31.1-2 (1997): 1-13
Binding, Paul, Dr{\'a}bek, Pavel and Huang, Yin . "On {N}eumann boundary value problems for some quasilinear elliptic equations" Electronic Journal of Differential Equations (1997): No. 05, approx. 11 pp. (electronic)
Binding, Paul, Dr{\'a}bek, Pavel and Huang, Yin . "On the {F}redholm alternative for the {$p$}-{L}aplacian" Proc. Amer. Math. Soc. 125.12 (1997): 3555-3559
Biles, D. C. and Binding, Paul. "On {C}arath\'eodory's conditions for the initial value problem" Proc. Amer. Math. Soc. 125.5 (1997): 1371-1376
Binding, Paul and Volkmer, Hans . "Eigencurves for two-parameter {S}turm-{L}iouville equations" SIAM Review. A Publication of the Society for Industrial and Applied Mathematics 38.1 (1996): 27-48
Binding, Paul and Ko{\v{s}}ir, Toma . "Second root vectors for multiparameter eigenvalue problems of {F}redholm type" Transactions of the American Mathematical Society 348.1 (1996): 229-249
Binding, Paul and Ye, Qiang . "Variational principles for indefinite eigenvalue problems" Linear Algebra and its Applications 218 (1995): 251-262
Binding, Paul. "A new angle on {S}turm-{L}iouville problems" The Rocky Mountain Journal of Mathematics 25.1 (1995): 51-56
Binding, Paul and Browne, Patrick. "Application of two parameter eigencurves to {S}turm-{L}iouville problems with eigenparameter-dependent boundary conditions" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 125.6 (1995): 1205-1218
Binding, Paul, Farenick, D. R. and Li, Chi . "A dilation and norm in several variable operator theory" Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 47.3 (1995): 449-461
Binding, Paul and Huang, Y. X. "Bifurcation from eigencurves of the {$p$}-{L}aplacian" Differential Integral Equations 8.2 (1995): 415-428
Binding, Paul and Huang, Y. X. "The principal eigencurve for the {$p$}-{L}aplacian" Differential Integral Equations 8.2 (1995): 405-414
Binding, Paul and Huang, Y. X. "Existence and nonexistence of positive eigenfunctions for the {$p$}-{L}aplacian" Proc. Amer. Math. Soc. 123.6 (1995): 1833-1838
Binding, Paul and Huang, Y. X. "Linked eigenvalue problems for the {$p$}-{L}aplacian" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 124.5 (1994): 1023-1036
Azizov, T. , Binding, Paul, Bogn{\'a}r, J. and Najman, B. . "Nondegenerate {J}ordan subspaces of selfadjoint operators in indefinite spaces" Linear Algebra and its Applications 207 (1994): 37-48
Binding, Paul, Browne, Patrick and Seddighi, K. . "Sturm-{L}iouville problems with eigenparameter dependent boundary conditions" Proceedings of the Edinburgh Mathematical Society. Series II 37.1 (1994): 57-72
Binding, Paul and Najman, Branko . "A variational principle in {K}re\u\i n space" Transactions of the American Mathematical Society 342.2 (1994): 489-499
Binding, Paul, Browne, Patrick and Ji, Xing . "A numerical method using the {P}r\"ufer transformation for the calculation of eigenpairs of two-parameter {S}turm-{L}iouville problems" IMA Journal of Numerical Analysis 13.4 (1993): 559-569
Binding, Paul and Volkmer, H. . "On the geometry of degree conditions for multiparameter oscillation theorems" Differential Integral Equations 6.2 (1993): 277-290
Binding, Paul and Ye, Qiang . "Some general local variational principles" Proc. Amer. Math. Soc. 114.1 (1992): 107-114
Binding, Paul and Volkmer, Hans . "On a problem of {R}. {G}. {D}. {R}ichardson" Proceedings of the Edinburgh Mathematical Society. Series II 35.3 (1992): 337-348
Herzog, Walter and Binding, Paul. "Predictions of antagonistic muscular activity using nonlinear optimization" Mathematical Biosciences 111.2 (1992): 217-229
Binding, Paul, Browne, Patrick and Seddighi, K. . "Two parameter asymptotic spectra" Results in Mathematics. Resultate der Mathematik 21.1-2 (1992): 12-23
Binding, Paul, Browne, Patrick, Huang, Y. X. and Picard, R. H. "On eigencurves of elliptic boundary value problems" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 118.1-2 (1991): 161-171
Binding, Paul. "More on cross products" The American Mathematical Monthly 98.9 (1991): 850-851
Binding, Paul and Ye, Qiang . "Variational principles without definiteness conditions" SIAM Journal on Mathematical Analysis 22.6 (1991): 1575-1583
Binding, Paul and Li, Chi . "Joint ranges of {H}ermitian matrices and simultaneous diagonalization" Linear Algebra and its Applications 151 (1991): 157-167
Binding, Paul and Browne, Patrick. "Asymptotics of eigencurves for second order ordinary differential equations. {II}" J. Differential Equations 89.2 (1991): 224-243
Binding, Paul and Sleeman, B. D. "Spectral decomposition of uniformly elliptic multiparameter eigenvalue problems" J. Math. Anal. Appl. 154.1 (1991): 100-115
Binding, Paul and Browne, Patrick. "Asymptotics of eigencurves for second order ordinary differential equations. {I}" J. Differential Equations 88.1 (1990): 30-45
Binding, Paul. "Simultaneous diagonalisation of several {H}ermitian matrices" SIAM Journal on Matrix Analysis and Applications 11.4 (1990): 531-536
Binding, Paul, Browne, Patrick and Picard, R. H. "Corrigendum: ``{S}pectral properties of two-parameter eigenvalue problems. {II}'' [{P}roc.\ {R}oy.\ {S}oc.\ {E}dinburgh {S}ect.\ {A} {\bf 106} (1987), no.\ 1-2, 39-51; \refmr {MR}0899939 (88m:47036)\endrefmr] by {B}inding and {B}rowne" Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 115.1-2 (1990): 87-90
Binding, Paul and Browne, Patrick. "Eigencurves for two-parameter selfadjoint ordinary differential equations of even order" J. Differential Equations 79.2 (1989): 289-303
Binding, Paul. "A canonical form for selfadjoint pencils in {H}ilbert space" Integral Equations and Operator Theory 12.3 (1989): 324-342
Binding, Paul and Browne, Patrick. "Classification of eigentuples for uniformly elliptic multiparameter problems" J. Math. Anal. Appl. 139.1 (1989): 268-281
Binding, Paul. "Multiparameter root vectors" Proceedings of the Edinburgh Mathematical Society. Series II 32.1 (1989): 19-29
Binding, Paul and Browne, Patrick. "Two parameter eigenvalue problems for matrices" Linear Algebra and its Applications 113 (1989): 139-157
Binding, Paul and Browne, Patrick. "Applications of two parameter spectral theory to symmetric generalised eigenvalue problems" Applicable Analysis. An International Journal 29.1-2 (1988): 107-142
Binding, Paul and Browne, Patrick. "Spectral properties of two-parameter eigenvalue problems. {II}" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 106.1-2 (1987): 39-51
Binding, Paul and Seddighi, K. . "Elliptic multiparameter eigenvalue problems" Proceedings of the Edinburgh Mathematical Society. Series II 30.2 (1987): 215-228
Binding, Paul and Seddighi, K. . "On root vectors of selfadjoint pencils" Journal of Functional Analysis 70.1 (1987): 117-125
Binding, Paul. "Erratum: ``{M}ultiparameter definiteness conditions. {II}'' [{P}roc.\ {R}oy.\ {S}oc.\ {E}dinburgh {S}ect.\ {A} {\bf 93} (1982/83), no.\ 1-2, 47-61; \refmr {MR}0688284 (84f:47055)\endrefmr]" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 103.3-4 (1986): 359
Binding, Paul, Browne, Patrick and Turyn, Lawrence . "Existence conditions for higher order eigensets of multiparameter operators" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 103.1-2 (1986): 137-146
Binding, Paul and Volkmer, Hans . "Existence and uniqueness of indexed multiparametric eigenvalues" J. Math. Anal. Appl. 116.1 (1986): 131-146
Binding, Paul. "Hermitian forms and the fibration of spheres" Proc. Amer. Math. Soc. 94.4 (1985): 581-584
Binding, Paul. "Indicial equivalents of multiparameter definiteness conditions in finite dimensions" Proceedings of the Edinburgh Mathematical Society. Series II 27.3 (1984): 283-296
Binding, Paul and Browne, Patrick. "Multiparameter {S}turm theory" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 99.1-2 (1984): 173-184
Binding, Paul, Browne, Patrick and Turyn, Lawrence . "Spectral properties of compact multiparameter operators" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 98.3-4 (1984): 291-303
Binding, Paul. "The inertia of a {H}ermitian pencil" Linear Algebra and its Applications 63 (1984): 179-191
Binding, Paul, Browne, Patrick and Turyn, Lawrence . "Existence conditions for eigenvalue problems generated by compact multiparameter operators" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 96.3-4 (1984): 261-274
Binding, Paul. "Nonuniform right definiteness" J. Math. Anal. Appl. 102.1 (1984): 233-243
Binding, Paul. "Perturbation and bifurcation of nonsingular multiparametric eigenvalues" Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods 8.4 (1984): 335-352
Binding, Paul. "Abstract oscillation theorems for multiparameter eigenvalue problems" J. Differential Equations 49.3 (1983): 331-343
Binding, Paul. "Dual variational approaches to multiparameter eigenvalue problems" J. Math. Anal. Appl. 92.1 (1983): 96-113
Binding, Paul. "Multiparameter definiteness conditions. {II}" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 93.1-2 (1982/83): 47-61
Binding, Paul. "Erratum: ``{O}n a problem of {B}. {D}. {S}leeman''" J. Math. Anal. Appl. 90.1 (1982): 270-271
Binding, Paul, K{\"a}llstr{\"o}m, A. and Sleeman, B. D. "An abstract multiparameter spectral theory" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 92.3-4 (1982): 193-204
Binding, Paul. "Multiparameter variational principles" SIAM Journal on Mathematical Analysis 13.5 (1982): 842-855
Binding, Paul. "Left definite multiparameter eigenvalue problems" Transactions of the American Mathematical Society 272.2 (1982): 475-486
Binding, Paul. "On a problem of {B}. {D}. {S}leeman" J. Math. Anal. Appl. 85.2 (1982): 291-307
Binding, Paul, Browne, Patrick and Turyn, Lawrence . "Existence conditions for two-parameter eigenvalue problems" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 91.1-2 (1981/82): 15-30
Binding, Paul. "Multiparameter definiteness conditions" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 89.3-4 (1981): 319-332
Binding, Paul and Browne, Patrick. "Spectral properties of two-parameter eigenvalue problems" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 89.1-2 (1981): 157-173
Binding, Paul. "On generalised and quadratic eigenvalue problems" Applicable Analysis. An International Journal 12.1 (1981): 27-45
Binding, Paul. "Variational methods for one and several parameter nonlinear eigenvalue problems" Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 33.1 (1981): 210-228
Binding, Paul. "Another positivity result for determinantal operators" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 86.3-4 (1980): 333-337
Binding, Paul and Browne, Patrick. "Comparison cones for multiparameter eigenvalue problems" J. Math. Anal. Appl. 77.1 (1980): 132-149
Binding, Paul. "On the use of degree theory for nonlinear multiparameter eigenvalue problems" J. Math. Anal. Appl. 73.2 (1980): 381-391
Binding, Paul. "Corrections to: ``{B}ounded variation evolution equations'' [{J}. {M}ath. {A}nal. {A}ppl. {\bf 48} (1974), 70-94;\ {MR} {\bf 50} \#10967]" J. Math. Anal. Appl. 74.2 (1980): 635-636
Binding, Paul. "The differential equation {$\dot x=f\circ x$}" J. Differential Equations 31.2 (1979): 183-199
Binding, Paul and Browne, Patrick. "Positivity results for determinantal operators" Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences 81.3-4 (1978): 267-271
Binding, Paul and Browne, Patrick. "A variational approach to multi-parameter eigenvalue problems in {H}ilbert space" SIAM Journal on Mathematical Analysis 9.6 (1978): 1054-1067
Binding, Paul and Browne, Patrick. "A variational approach to multiparameter eigenvalue problems for matrices" SIAM Journal on Mathematical Analysis 8.5 (1977): 763-777
Binding, Paul. "On infinite-dimensional differential equations" J. Differential Equations 24.3 (1977): 349-354
Binding, Paul and Browne, Patrick. "{$L\sp{p}$} spaces generated by certain operator valued measures" Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 19.4 (1976): 403-416
Binding, Paul. "Singularly perturbed optimal control problems. {I}. {C}onvergence" SIAM J. Control Optimization 14.4 (1976): 591-612
Binding, Paul and Browne, Patrick. "{$L\sp{p}$} spaces from matrix measures" Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 18.1 (1975): 19-25
Binding, Paul. "Bounded variation evolution equations" J. Math. Anal. Appl. 48 (1974): 70-94
Binding, Paul, Hoskins, W. D. and Ponzo, P. J. "Bounds for characteristic values of positive definite matrices" Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 15 (1972): 51-56
Book
Binding, Paul, Browne, Patrick and Watson, Bruce. "Spectral isomorphisms between generalized {S}turm-{L}iouville problems" Operations Theory, Advanced Applications, 130, Birkh\"auser (2002): 135-152
Binding, Paul and Hryniv, R.. "Full- and partial-range completeness" Operations Theory, Advanced Applications, 130, Birkh\"auser (2002): 121-133
Binding, Paul and Hryniv, R.. Elliptic spectral problems of higher order with eigenparameter dependent boundary conditions 124, Birkh\"auser (2001): 145-153
Binding, Paul and Huang, Y. X. Two parameter problems for the {$p$}-{L}aplacian de Gruyter (1996): 891-900
Binding, Paul and Najman, B. . Regularity of finite type critical points for self-adjoint operators in {K}re\u\i n space 80, Birkh\"auser (1995): 79-89
Binding, Paul. Indefinite {S}turm-{L}iouville theory via examples of two-parameter eigencurves 254, Longman Sci. Tech. (1991): 38-49
Binding, Paul and Browne, Patrick. A definiteness result for determinantal operators 1032, Springer (1983): 17-30

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