On the Bézout equation in the ring of periodic distributions
Rudolf Rupp ; Amol Sasane
Topological Algebra and its Applications, Tome 4 (2016), p. 1-8 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:277085
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     volume = {4},
     year = {2016},
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     zbl = {06624320},
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Rudolf Rupp; Amol Sasane. On the Bézout equation in the ring of periodic distributions. Topological Algebra and its Applications, Tome 4 (2016) pp. 1-8. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_taa-2016-0001/

[1] H. Bass. K-theory and stable algebra. Inst. Hautes Études Sci. Publ. Math., No. 22, 5-60, 1964. | Zbl 0248.18025

[2] N.K. Bose. Applied Multidimensional Systems Theory. Reidel, Dordrecht, 1984. | Zbl 0574.93031

[3] W.F. Donoghue, Jr., Distributions and Fourier Transforms. Pure and Applied Mathematics 32, Academic Press, New York and London, 1969. | Zbl 0188.18102

[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. | Zbl 0980.16001

[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. | Zbl 0533.46046

[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. | Zbl 1217.46022

[10] F. Trèves. Topological Vector Spaces, Distributions and Kernels. Unabridged republication of the 1967 original. Dover Publications, Mineola, NY, 2006.