Login



Other Articles by Authors

Vladimir Vasilyev



Authors and WSEAS

Vladimir Vasilyev


WSEAS Transactions on Mathematics


Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 16, 2017

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 16, 2017



Discrete Operators in Canonical Domains

AUTHORS: Vladimir Vasilyev

Download as PDF

ABSTRACT: In this paper, we consider a certain class of discrete pseudo-differential operators in a sharp convex cone and describe their invertibility conditions in L2-spaces. For this purpose we introduce a concept of periodic wave factorization for elliptic symbol and show its applicability for the studying.

KEYWORDS: Discrete operator, Multidimensional periodic Riemann problem, Periodic wave factorization, Invertibility

REFERENCES:

[1] M. E. Taylor, Pseudodifferential Operators, Princeton Univ. Press, Princeton 1981

[2] F. Treves, Introduction to Pseudodifferential Operators and Fourier Integral Operators, Springer, New York 1980

[3] G. Eskin, Boundary Value Problems for Elliptic Pseudodifferential Equations, AMS, Providence 1981

[4] M. A. Shubin, Pseudodifferential Operators and Spectral Theory, Springer, Berlin–Heidelberg 2001

[5] F. D. Gakhov, Boundary Value Problems, Dover Publications, New York 1981

[6] N. I. Muskhelishvili, Singular Integral Equations, North Holland, Amsterdam 1976

[7] S. Bochner and W. T. Martin, Several Complex Variables, Princeton Univ. Press, Princeton, 1948

[8] V. S. Vladimirov, Methods of the Theory of Functions of Many Complex Variables, Dover Publications, New York (2007)

[9] V. B. Vasil’ev, Wave Factorization of Elliptic Symbols: Theory and Applications, Kluwer Academic Publishers, Dordrect–Boston– London 2000

[10] A. V. Vasilyev and V. B. Vasilyev, Discrete singular operators and equations in a half-space, Azerb. J. Math. 3, 2013, pp. 84–93.

[11] A. V. Vasilyev and V. B. Vasilyev, Discrete singular integrals in a half-space. In: Mityushev, V., Ruzhansky, M. (eds.) Current Trends in Analysis and Its Applications. Proc. 9th ISAAC Congress, Krakow, Poland, 2013, ´ pp. 663–670. Birkhauser, ¨ Basel 2015. Series: Trends in Mathematics. Research Perspectives.

[12] A. V. Vasilyev and V. B. Vasilyev, Periodic Riemann problem and discrete convolution equations, Differential Equat. 51, 2015, pp. 652–660.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 16, 2017, Art. #23, pp. 197-201


Copyright © 2017 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

Bulletin Board

Currently:

The editorial board is accepting papers.


WSEAS Main Site