An integral representation of an eigenfunction of the Laplacian on the Euclidean space

zbMath0269.35012MaRDI QIDQ2563245

Katsuhiro Minemura, Kiyosato Okamoto, Michihiko Hashizume, Atsutaka Kowata

Publication date: 1972

Published in: Hiroshima Mathematical Journal (Search for Journal in Brave)

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Estimates of eigenvalues in context of PDEs (35P15) Integral representations of solutions to PDEs (35C15) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Integral representations, integral operators, integral equations methods in higher dimensions (31B10)

Related Items

Eigenfunctions of the Laplace-Beltrami operator on harmonic \(NA\) groups ⋮ On the Fourier-Borel transformations of analytic functionals on the complex sphere ⋮ On a Bargmann-type transform and a Hilbert space of holomorphic functions ⋮ Generalized Laplacians for generalized Poisson-Cauchy transforms on classical domains ⋮ Special function representations of the Poisson kernel on hyperbolic spaces ⋮ Integral representations and Liouville theorems for solutions of periodic elliptic equations ⋮ Eigenspaces of the Laplacian ; integral representations and irreducibility ⋮ Hecke-Bochner identity and eigenfunctions associated to Gelfand pairs on the Heisenberg group