On the Bézout equation in the ring of periodic distributions

Rudolf Rupp; Amol Sasane

Topological Algebra and its Applications (2016)

  • Volume: 4, Issue: 1, page 1-8
  • ISSN: 2299-3231

Abstract

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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.

How to cite

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Rudolf Rupp, and Amol Sasane. "On the Bézout equation in the ring of periodic distributions." Topological Algebra and its Applications 4.1 (2016): 1-8. <http://eudml.org/doc/277085>.

@article{RudolfRupp2016,
abstract = {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.},
author = {Rudolf Rupp, Amol Sasane},
journal = {Topological Algebra and its Applications},
keywords = {periodic distributions; Fourier series; Bass stable rank; topological stable rank; Bézout equation},
language = {eng},
number = {1},
pages = {1-8},
title = {On the Bézout equation in the ring of periodic distributions},
url = {http://eudml.org/doc/277085},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Rudolf Rupp
AU - Amol Sasane
TI - On the Bézout equation in the ring of periodic distributions
JO - Topological Algebra and its Applications
PY - 2016
VL - 4
IS - 1
SP - 1
EP - 8
AB - 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.
LA - eng
KW - periodic distributions; Fourier series; Bass stable rank; topological stable rank; Bézout equation
UR - http://eudml.org/doc/277085
ER -

References

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  1. [1] H. Bass. K-theory and stable algebra. Inst. Hautes Études Sci. Publ. Math., No. 22, 5-60, 1964.  Zbl0248.18025
  2. [2] N.K. Bose. Applied Multidimensional Systems Theory. Reidel, Dordrecht, 1984.  Zbl0574.93031
  3. [3] W.F. Donoghue, Jr., Distributions and Fourier Transforms. Pure and Applied Mathematics 32, Academic Press, New York and London, 1969.  Zbl0188.18102
  4. [4] J.J. Duistermaat and J.A.C. Kolk. Distributions. Theory and Applications. Birkhäuser, Boston, MA, 2010.  
  5. [5] L. Hörmander. Generators for some rings of analytic functions. Bull. Am. Math. Soc., 73:943–949, 1967. [Crossref] 
  6. [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. [7] T.Y. Lam. A first course in noncommutative rings. Second edition, Graduate Texts in Mathematics Volume 131, Springer- Verlag, New York, 2001.  Zbl0980.16001
  8. [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.  Zbl0533.46046
  9. [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.  Zbl1217.46022
  10. [10] F. Trèves. Topological Vector Spaces, Distributions and Kernels. Unabridged republication of the 1967 original. Dover Publications, Mineola, NY, 2006.  

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