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An extension of solutions to convolution equations with the loss of smoothness
Homogeneous convolution equations mean periodic functions zeros of entire functions
2012/6/19
In the present paper the smoothness loss of an extension of solutions to convolution equations is studied. Also examples for some kinds of convolvers are given.
Abstract: In a convolution semigroup over a locally compact group, measurability of the translation by a fixed element implies continuity. In other words, the measurable centre coincides with the topo...
Convolution powers in the operator-valued framework
Convolution powers the operator-valued framework Operator Algebras
2011/9/9
Abstract: We consider the framework of an operator-valued noncommutative probability space over a unital C*-algebra B. We show how for a B-valued distribution \mu one can define convolution powers wit...
Completely bounded representations of convolution algebras of locally compact quantum groups
Locally compact quantum group Fourier algebra completely bounded homomorphism corepresentation amenability
2011/9/1
Abstract: Given a locally compact quantum group $\G$, we study the question of when completely bounded homomorphisms $\pi:L^1(\mathbb G)\rightarrow\mathcal B(H)$ are similar to *-homomorphisms. By ana...
Measurement error and convolution in generalized functions spaces
Measurement error convolution generalized functions spaces
2010/12/9
This paper considers convolution equations that arise from problems such as deconvolution and non-parametric regression with errors in variables. The equations are examined in spaces of generalized fu...
Continuity of Pseudo-Differential Operator $h_{\mu,a}$ Involving Hankel Translation and Hankel Convolution on Some Gevrey Spaces
Hankel transformation Hankel translation Hankel convolu-tion Pseudo-differential operator
2010/12/9
The Pseudo-Differential Operator (p.d.o.) hμ,a associated with the Bessel Operator involving the symbol a(x, y) whose derivatives satisfy certain growth conditions depending on some increasing sequenc...
SINGULAR MEASURES AND CONVOLUTION OPERATORS
Hardy--Littlewood maximal function Weak type inequalities Singular measures Convolution operators
2007/12/11
We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type $(1,1)$ inequalities. As an applicat...
ABSOLUTELY REPRESENTING SYSTEMS AND CONVOLUTION OPERATORS IN THE COMPLEX DOMAIN
CONVOLUTION OPERATORS ABSOLUTELY REPRESENTING SYSTEMS COMPLEX DOMAIN
2010/3/17
The author suggests a method of characterizing of the kernel of a convolution-type operator. The method is based on the exact description of nontrivial expansions of zero of an absolutely representing...