St. Petersburg Mathematical Journal

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ISSN 1547-7371(e) ISSN 1061-0022(p)

Some functional-difference equations solvable in finitary functions

Author(s): E. A. Gorin
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 18 (2006), nomer 5.
Journal: St. Petersburg Math. J. 18 (2007), 779-796.
MSC (2000): Primary 34K99, 32A15
Posted: August 9, 2007
MathSciNet review: 2301043
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: The following equation is considered: $q(-i\partial/\partial x)u(x)=(f*u)(Ax)$ , where is a polynomial with complex coefficients, is a compactly supported distribution, and $A:\mathbb{R}^n\to\mathbb{R}^n$ is a linear operator whose complexification has no spectrum in the closed unit disk. It turns out that this equation has a (smooth) solution with compact support. In the one-dimensional case, this problem was treated earlier in detail by V. A. Rvachev and V. L. Rvachev and their numerous students.

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