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august 2010 Convolution equations on spaces of quasi-nuclear functions of a given type and order
Vinícius V. Fávaro
Bull. Belg. Math. Soc. Simon Stevin 17(3): 535-569 (august 2010). DOI: 10.36045/bbms/1284570737

Abstract

In this article we prove existence and approximation results for convolution equations on the spaces of $\left( s;\left( r,q\right) \right) $-quasi-nuclear mappings of a given type and order on a Banach space $E$. As special case this yields results for partial differential equations with constant coefficients for entire functions on finite-dimensional complex Banach spaces. We also prove division theorems for $\left( s;m\left( r,q\right) \right) $-summing functions of a given type and order, that are essential to prove the existence and approximation results.

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Vinícius V. Fávaro. "Convolution equations on spaces of quasi-nuclear functions of a given type and order." Bull. Belg. Math. Soc. Simon Stevin 17 (3) 535 - 569, august 2010. https://doi.org/10.36045/bbms/1284570737

Information

Published: august 2010
First available in Project Euclid: 15 September 2010

zbMATH: 1211.46038
MathSciNet: MR2731373
Digital Object Identifier: 10.36045/bbms/1284570737

Subjects:
Primary: 46G20
Secondary: 46G25

Keywords: ‎Banach spaces , convolution equations , division theorems , homogeneous polynomials

Rights: Copyright © 2010 The Belgian Mathematical Society

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Vol.17 • No. 3 • august 2010
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