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# Boundary problems for the wave equation with the Lévy Laplacian in Shilov's class

### Abstract

We present solutions to some boundary value and initial-boundary value problems for the "wave" equation with the infinite dimensional L\'evy Laplacian $\Delta _L$ $$\frac{\partial^2 U(t,x)}{\partial t^2}=\Delta_LU(t,x)$$ in the Shilov class of functions.

Key words: L´evy Laplacian, hyperbolic equations, wave equation, boundary problems, initial-boundary value problems.

### Article Information

 Title Boundary problems for the wave equation with the Lévy Laplacian in Shilov's class Source Methods Funct. Anal. Topology, Vol. 16 (2010), no. 3, 197-202 MathSciNet MR2743587 Copyright The Author(s) 2010 (CC BY-SA)

### Authors Information

S. Albeverio
Institut fur Angewandte Mathematik, Universitat Bonn, Wegelerstr.6, D-53115 Bonn; SFB 611, HCM, IZKS, Bonn, Germany; CERFIM, Locarno and USI, Switzerland

Ya. I. Belopolskaya
St. Petersburg State University for Architecture and Civil Engineering, 2-ja Krasnoarmejskaja 4, St. Petersburg, 190005, Russia

M. N. Feller
UkrNII RESURS, Kyiv, Ukraine

### Citation Example

S. Albeverio, Ya. I. Belopolskaya, and M. N. Feller, Boundary problems for the wave equation with the Lévy Laplacian in Shilov's class, Methods Funct. Anal. Topology 16 (2010), no. 3, 197-202.

### BibTex

@article {MFAT508,
AUTHOR = {Albeverio, S. and Belopolskaya, Ya. I. and Feller, M. N.},
TITLE = {Boundary problems for the  wave equation with the Lévy  Laplacian in  Shilov's class},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {16},
YEAR = {2010},
NUMBER = {3},
PAGES = {197-202},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=508},
}