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

Authors

  • M. N. Feller 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 https://orcid.org/0000-0002-8303-2571
  • S. Albeverio UkrNII RESURS, Kyiv, Ukraine 

DOI:

Keywords:

L´evy Laplacian, hyperbolic equations, wave equation, boundary problems, initial-boundary value problems

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.

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Published

2010-09-25

Issue

Vol. 16 No. 3 (2010)

Section

Articles

How to Cite

Feller, M. N., et al. “Boundary Problems for the Wave Equation With the Lévy Laplacian in Shilov’s Class”. Methods of Functional Analysis and Topology, vol. 16, no. 3, Sept. 2010, pp. 197-02, https://zen.imath.kiev.ua/index.php/mfat/article/view/451.