AUTHORS: Vladimir Vasilyev
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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.