Abstract multiparameter theory. I

DOI10.1016/0022-247X(77)90065-8zbMath0357.47015MaRDI QIDQ1238124

Patrick J. Browne

Publication date: 1977

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Spectrum, resolvent (47A10) Linear symmetric and selfadjoint operators (unbounded) (47B25) Tensor products in functional analysis (46M05) Ordinary differential operators (34L99) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)

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An abstract multiparameter spectral theory ⋮ The spectrum of multiparameter problems in Hilbert space ⋮ Multiparameter spectral problems and commuting extensions of symmetric operators ⋮ Uniform convergence of multiparameter eigenfunction expansions ⋮ Regular multiparameter eigenvalue problems with several parameters in the boundary conditions ⋮ Product formulas and convolutions for Laplace-Beltrami operators on product spaces: beyond the trivial case ⋮ Abstract multiparameter theory. III ⋮ On the use of degree theory for nonlinear multiparameter eigenvalue problems ⋮ Comparison cones for multiparameter eigenvalue problems ⋮ Singular Hamiltonian system with several spectral parameters ⋮ Multiparameter spectral theory of singular differential operators ⋮ On a problem of B. D. Sleeman ⋮ On multiparameter theory ⋮ Left Definite Multiparameter Eigenvalue Problems ⋮ Spectral decomposition of uniformly elliptic multiparameter eigenvalue problems ⋮ Eigenvector expansion of multiparameter spectral problems ⋮ Abstract multiparameter theory. II ⋮ Multiparameter spectral theory in Hilbert space ⋮ On generalised and quadratic eigenvalue problems ⋮ Singular multiparameter dynamic equations with distributional potentials on time scales ⋮ NON-LINEAR MULTIPARAMETER EIGENVALUE PROBLEMS ⋮ Multiparameter definiteness conditions ⋮ On the completeness of eigenvectors of right definite multiparameter problems

Cites Work

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• Multiparameter eigenvalue problems. Volume I: Matrices and compact operators
• The completeness and expansion theorems associated with the multi- parameter eigenvalue problem in ordinary differential equations
• A singular multi-parameter eigenvalue problem in second order ordinary differential equations
• A multi-parameter eigenvalue problem
• Multiparameter spectral theory
• The Two-Parameter Sturm-Liouville Problem for Ordinary Differential Equations. II
• Completeness and Expansion Theorems for a Two-Parameter Eigenvalue Problem in Ordinary Differential Equations Using Variational Principles

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