Eigenfunction expansion associated with the operator-$\Delta$ in the exterior domain

DOI10.3792/pja/1195522929zbMath0143.14504OpenAlexW2001292447MaRDI QIDQ5518742

Yasushi Shizuta

Publication date: 1963

Published in: Proceedings of the Japan Academy, Series A, Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pja/1195522929

zbMATH Keywords

partial differential equations

Related Items

Eigenfunction expansions associated with the Laplacian for certain domains with infinite boundaries. I ⋮ On the theory of linear equations and Fredholm determinants ⋮ Eigenfunction expansions for symmetric systems of first order in the half-space $R_ + ^n $ ⋮ Generalized Potentials and Obstacle Scattering ⋮ Outgoing solutions for perturbations of -\(\Delta\) with applications to spectral and scattering theory ⋮ Eigenfunction expansions and spectral projections for isotropic elasticity outside an obstacle ⋮ Eigenfunction expansions for symmetric systems of first order in the half-space \(R^n\) ⋮ Eigenfunction expansions and scattering theory for the wave equation in an exterior region ⋮ Orthogonality of the eigenfunctions for the exterior problem connected with \(-\Delta\) ⋮ Scattering theory with two Hilbert spaces ⋮ Eigenfunction expansions and scattering theory for perturbations of - \(\Delta\) ⋮ Spectral and scattering theory for symmetric hyperbolic systems in an exterior domain ⋮ The Green function for \(\sum\limits_{n=1}^3 (i \;{\partial \over {\partial x_n}} - b_n)^2 u = \lambda u\) in the exterior domain and its application to the eigenfunction expansion ⋮ On the absolute and uniform convergence of generalized Fourier integrals in vector eigenfunctions of the operator of elasticity theory in an unbounded domain

Cites Work

• Eigenfunction expansions associated with the Schrödinger operators and their applications to scattering theory
• Über das asymptotische Verhalten der Lösungen von \(\Delta u+\lambda u=0\) in unendlichen Gebieten
• The wave equation in exterior domains
• Sur l'analyticité de la fonction spectrale de l'opérateur $\Delta$ relatif au problème extérieur
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