On the Bézout equation in the ring of periodic distributions

• Autorzy: Rudolf Rupp , Amol Sasane
• Języki publikacji: EN

Abstrakty

EN

A corona type theorem is given for the ring D'A(Rd) of periodic distributions in Rd in terms of the sequence of Fourier coefficients of these distributions,which have at most polynomial growth. It is also shown that the Bass stable rank and the topological stable rank of D'A(Rd) are both equal to 1.

Słowa kluczowe

EN

periodic distributions; Fourier series; Bass stable rank; topological stable rank; Bézout equation

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2016
• Tom: 4
• Numer: 1
• Strony: 1-8

Daty

otrzymano

2015-06-04

zaakceptowano

2015-10-18

online

2016-04-15

Twórcy

autor

Rudolf Rupp

• Fakultät für Angewandte Mathematik, Physik und Allgemeinwissenschaften, TH-Nürnberg, Kesslerplatz 12, D- 90489 Nürnberg, Germany

autor

Amol Sasane

• Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom

Bibliografia

• [1] H. Bass. K-theory and stable algebra. Inst. Hautes Études Sci. Publ. Math., No. 22, 5-60, 1964.
• [2] N.K. Bose. Applied Multidimensional Systems Theory. Reidel, Dordrecht, 1984.
• [3] W.F. Donoghue, Jr., Distributions and Fourier Transforms. Pure and Applied Mathematics 32, Academic Press, New York and London, 1969.
• [4] J.J. Duistermaat and J.A.C. Kolk. Distributions. Theory and Applications. Birkhäuser, Boston, MA, 2010.
• [5] L. Hörmander. Generators for some rings of analytic functions. Bull. Am. Math. Soc., 73:943–949, 1967. [Crossref]
• [6] L. Hörmander. The Analysis of Linear Partial Differential Operators. I. Distribution Theory and Fourier Analysis. Second edition. Springer Study Edition, Springer-Verlag, Berlin, 1990.
• [7] T.Y. Lam. A first course in noncommutative rings. Second edition, Graduate Texts in Mathematics Volume 131, Springer- Verlag, New York, 2001.
• [8] M.A. Rieffel. Dimension and stable rank in the K-theory of C*-algebras. Proceedings of the London Mathematical Society, (3), 46:301-333, no. 2, 1983.
• [9] S. Maad Sasane and A.J. Sasane. Generators for rings of compactly supported distributions. Integral Equations Operator Theory, 69:63-71, no. 1, 2011.
• [10] F. Trèves. Topological Vector Spaces, Distributions and Kernels. Unabridged republication of the 1967 original. Dover Publications, Mineola, NY, 2006.

Identyfikatory

DOI

10.1515/taa-2016-0001