Abstract:
The dual to a weighted space G of infinitely smooth functions on the real axis is described by means of the Fourier–Laplace transformation. This result is used in the study of the surjectivity in G of an infinite-order linear differential operator with constant coefficients.
Citation:
I. Kh. Musin, “Fourier–Laplace transformation of functionals on a weighted space of infinitely smooth functions”, Sb. Math., 191:10 (2000), 1477–1506
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\by I.~Kh.~Musin
\paper Fourier--Laplace transformation of functionals on a~weighted space of infinitely smooth functions
\jour Sb. Math.
\yr 2000
\vol 191
\issue 10
\pages 1477--1506
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Linking options:
https://www.mathnet.ru/eng/sm516
https://doi.org/10.1070/sm2000v191n10ABEH000516
https://www.mathnet.ru/eng/sm/v191/i10/p57
This publication is cited in the following 13 articles:
I. Kh. Musin, “On Fourier–Laplace transform of a class of generalized functions”, Ufa Math. J., 12:4 (2020), 78–89
I. Kh. Musin, “O prostranstve funktsii, golomorfnykh v ogranichennoi vypukloi oblasti i gladkikh vplot do granitsy, i ego sopryazhennom”, Vladikavk. matem. zhurn., 22:3 (2020), 100–111
I. Kh. Musin, “Approximation of infinitely differentiable functions on the real line by polynomials in weighted spaces”, J. Math. Sci. (N. Y.), 257:3 (2021), 329–333
Fam Ch.T., “Opisanie sopryazhennykh k prostranstvu freshe beskonechno differentsiruemykh funktsii s vesovymi otsenkami vsekh proizvodnykh v \it{r}^{\it{n}}”, Izvestiya vysshikh uchebnykh zavedenii. Severo-Kavkazskii region. Seriya: Estestvennye nauki, 2011, no. 6, 19–23
Description of the dual space for a frechet space of infinitely differentiable functions with weighted estimates of all derivatives in r<sup>n</sup>
I. Kh. Musin, S. V. Popenov, “O vesovom prostranstve beskonechno differentsiruemykh funktsii v Rn”, Ufimsk. matem. zhurn., 2:3 (2010), 54–62
I. Kh. Musin, P. V. Fedotova, “A Theorem of Paley–Wiener Type for Ultradistributions”, Math. Notes, 85:6 (2009), 848–867
A. V. Abanin, “O multiplikatorakh prostranstva tselykh funktsii, zadavaemogo neradialnym dvuchlennym vesom”, Vladikavk. matem. zhurn., 10:4 (2008), 10–16
S. V. Panyushkin, “Generalized Fourier transform and its applications”, Math. Notes, 79:4 (2006), 537–550
Musin I.K., “Description of the kernel of a differential operator”, Dokl. Math., 69:3 (2004), 381–384
A. V. Abanin, Yu. S. Nalbandyan, I. S. Shabarshina, “Prodolzhenie beskonechno differentsiruemykh funktsii do tselykh s soglasovannymi otsenkami rosta i teoremy tipa Peli—Vinera— Shvartsa”, Vladikavk. matem. zhurn., 6:2 (2004), 3–9
I. Kh. Musin, “Fourier–Laplace transformation of functionals on a weighted space of infinitely smooth functions on Rn”, Sb. Math., 195:10 (2004), 1477–1501
I. Kh. Musin, “On the Representation of Infinitely Differentiable Functions by Series of Exponentials”, Math. Notes, 73:3 (2003), 370–382
I. Kh. Musin, “Surjectivity of Linear Differential Operators in a Weighted Space of Infinitely Differentiable Functions”, Math. Notes, 71:5 (2002), 649–660
Citation in format AMSBIB
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