Some functional-difference equations solvable in finitary functions
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E. A. Gorin
Translated by: S. V. Kislyakov - St. Petersburg Math. J. 18 (2007), 779-796
- DOI: https://doi.org/10.1090/S1061-0022-07-00973-9
- Published electronically: August 9, 2007
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Abstract:
The following equation is considered: $q(-i\partial /\partial x)u(x)=(f*u)(Ax)$, where $q$ is a polynomial with complex coefficients, $f$ 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 $u(x)$ 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.References
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Bibliographic Information
- E. A. Gorin
- Affiliation: Department of Mathematics, Moscow State Pedagogical University, Ulitsa Malaya Pirogovskaya 1, Moscow 119882, Russia
- Email: evgeny.gorin@mtu-net.ru
- Received by editor(s): April 22, 2006
- Published electronically: August 9, 2007
- © Copyright 2007 American Mathematical Society
- Journal: St. Petersburg Math. J. 18 (2007), 779-796
- MSC (2000): Primary 34K99, 32A15
- DOI: https://doi.org/10.1090/S1061-0022-07-00973-9
- MathSciNet review: 2301043
Dedicated: Dedicated to the 100th anniversary of B. Ya. Levin’s birth