Convolution equations in spaces of distributions with one-sided bounded support
HTML articles powered by AMS MathViewer
- by R. Shambayati and Z. Zielezny PDF
- Trans. Amer. Math. Soc. 289 (1985), 707-713 Request permission
Abstract:
Let $\mathcal {D}\prime (0,\infty )$ be the space of distributions on $R$ with support in $[0,\infty )$ and $\mathcal {S}\prime (0,\infty )$ its subspace consisting of tempered distributions. We characterize the distributions $S \in \mathcal {D}\prime (0,\infty )$ for which $S \ast \mathcal {D}\prime (0,\infty ) = \mathcal {D}\prime (0,\infty )$, where $\ast$ is the convolution. We also characterize the distributions $S \in \mathcal {S}\prime (0,\infty )$ for which $S \ast \mathcal {S}\prime (0,\infty ) = \mathcal {S}\prime (0,\infty )$.References
- L. Ehrenpreis, Solution of some problems of division. IV. Invertible and elliptic operators, Amer. J. Math. 82 (1960), 522–588. MR 119082, DOI 10.2307/2372971
- Lars Hörmander, On the range of convolution operators, Ann. of Math. (2) 76 (1962), 148–170. MR 141984, DOI 10.2307/1970269
- J. Mikusiński, Une simple démonstration du théorème de Titchmarsh sur la convolution, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 7 (1959), 715–717 (unbound insert) (French, with Russian summary). MR 0111996
- Laurent Schwartz, Théorie des distributions. Tome II, Publ. Inst. Math. Univ. Strasbourg, vol. 10, Hermann & Cie, Paris, 1951 (French). MR 0041345
- R. Shambayati and Z. Zieleźny, On Fourier transforms of distributions with one-sided bounded support, Proc. Amer. Math. Soc. 88 (1983), no. 2, 237–243. MR 695250, DOI 10.1090/S0002-9939-1983-0695250-3 E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Clarendon Press, Oxford, 1937.
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 289 (1985), 707-713
- MSC: Primary 46F10; Secondary 45E10, 46F12
- DOI: https://doi.org/10.1090/S0002-9947-1985-0784010-7
- MathSciNet review: 784010