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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
  • MATH211 - Linear Methods I
Representative Publications:
Journal Paper
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, 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 {\'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. "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 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. "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
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 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
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 Najman, Branko . "The minimal index of a self-adjoint pencil" Glasnik Matemati\v cki. Serija III 35(55).1 (2000): 25-44
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, 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 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. "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, 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, 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 Browne, Patrick. "Left definite {S}turm-{L}iouville problems with eigenparameter dependent boundary conditions" Differential Integral Equations 12.2 (1999): 167-182
Binding, Paul and Volkmer, Hans . "A spectrum determined by eigencurves" Mathematische Nachrichten 202 (1999): 5-15
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, 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. "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
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 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 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 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. "A new angle on {S}turm-{L}iouville problems" The Rocky Mountain Journal of Mathematics 25.1 (1995): 51-56
Binding, Paul and Ye, Qiang . "Variational principles for indefinite eigenvalue problems" Linear Algebra and its Applications 218 (1995): 251-262
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. "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
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 Seddighi, K. . "Sturm-{L}iouville problems with eigenparameter dependent boundary conditions" Proceedings of the Edinburgh Mathematical Society. Series II 37.1 (1994): 57-72
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 and Volkmer, H. . "On the geometry of degree conditions for multiparameter oscillation theorems" Differential Integral Equations 6.2 (1993): 277-290
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, Browne, Patrick and Seddighi, K. . "Two parameter asymptotic spectra" Results in Mathematics. Resultate der Mathematik 21.1-2 (1992): 12-23
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 and Browne, Patrick. "Asymptotics of eigencurves for second order ordinary differential equations. {II}" J. Differential Equations 89.2 (1991): 224-243
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, 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 and Li, Chi . "Joint ranges of {H}ermitian matrices and simultaneous diagonalization" Linear Algebra and its Applications 151 (1991): 157-167
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, 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. "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. "Multiparameter root vectors" Proceedings of the Edinburgh Mathematical Society. Series II 32.1 (1989): 19-29
Binding, Paul and Browne, Patrick. "Classification of eigentuples for uniformly elliptic multiparameter problems" J. Math. Anal. Appl. 139.1 (1989): 268-281
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. "Eigencurves for two-parameter selfadjoint ordinary differential equations of even order" J. Differential Equations 79.2 (1989): 289-303
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 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 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 Volkmer, Hans . "Existence and uniqueness of indexed multiparametric eigenvalues" J. Math. Anal. Appl. 116.1 (1986): 131-146
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. "Hermitian forms and the fibration of spheres" Proc. Amer. Math. Soc. 94.4 (1985): 581-584
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. "The inertia of a {H}ermitian pencil" Linear Algebra and its Applications 63 (1984): 179-191
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, 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. "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. "On a problem of {B}. {D}. {S}leeman" J. Math. Anal. Appl. 85.2 (1982): 291-307
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, 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. "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 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. "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. "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 generated by certain operator valued measures" Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 19.4 (1976): 403-416
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 130, Birkh\"auser (2002): 135-152
Binding, Paul and Hryniv, R.. Full- and partial-range completeness 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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