Equicontinuity and Convergent Sequences in the Spaces O′_C and O_M

• Autorzy: Kisyński J.

Identyfikatory

DOI

10.4064/ba59-3-5

• Języki publikacji: EN

Abstrakty

EN

Characterizations of equicontinuity and convergent sequences are given for the space O′_C(Rⁿ) of rapidly decreasing distributions and the space O_M(Rⁿ) of slowly increasing infinitely differentiable functions.

Słowa kluczowe

EN

slowly increasing function; rapidly decreasing distribution; convolution; multiplier; Fourier transformation; distribution as a sum of derivatives of continuous functions

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: Vol. 59, no 3
• Strony: 223--235
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Kisyński J.

• Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland

Bibliografia

• [K1] J. Kisynski, Convolution semigroups of rapidly decreasing distributions, preprint, Inst. Math., Polish Acad. Sci., 2010, 20 pp.
• [K2] —, The Petrovski˘ı condition and rapidly decreasing distributions, preprint, Inst. Math., Polish Acad. Sci., 2011, 17 pp.
• [P] I. G. Petrovski˘ı, Über das Cauchysche Problem für ein System linearer partieller Differentialgleichungen im Gebiete der nichtanalytischen Funktionen, Bull. Univ. d’État de Moscou 1 (1938), no. 7, 1–74.
• [S] H. Schaefer, Topological Vector Spaces, Macmillan, New York and Collier-Macmillan, London, 1966.
• [S1] L. Schwartz, Les équations d’évolution liées au produit de composition, Ann. Inst. Fourier (Grenoble) 2 (1950), 19–49.
• [S2] —, Théorie des Distributions, nouvelle éd., Hermann, Paris, 1966.
• [R] J. Rauch, Partial Differential Equations, Springer, 1991.
• [T] F. Treves, Topological Vector Spaces, Distributions and Kernels, Academic Press, 1967.
• [Y] K. Yosida, Functional Analysis, 6th ed., Springer, 1980.