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Riesz–Kolmogorov Type Compactness Criteria in Function Spaces with Applications
We present forms of the classical Riesz–Kolmogorov theorem for compactness that are applicable in a wide variety of settings. In particular, our...
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Continuity estimates for Riesz potentials on polygonal boundaries
Riesz potentials are well known objects of study in the theory of singular integrals that have been the subject of recent, increased interest from...
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Riesz–Zygmund means and trigonometric approximation in Morrey spaces
We estimate best approximations and moduli of smoothness of functions in Morrey spaces variable exponent spaces by norms of derivatives of...
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Riesz bases by replacement
In this paper we provide a method for constructing new Riesz bases on separable Hilbert spaces and we use it to prove sufficient conditions for the...
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Large time behaviour of a conservation law regularised by a Riesz-Feller operator: the sub-critical case
We study the large time behaviour of the solutions of a nonlocal regularisation of a scalar conservation law. This regularisation is given by a...
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The Riesz–Zygmund Sums of Fourier–Chebyshev Rational Integral Operators and Their Approximation Properties
Studying the approximation properties of a certain Riesz–Zygmund sum of Fourier–Chebyshev rational integral operators with constraints on the number...
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An adaptive finite element method for Riesz fractional partial integro-differential equations
The Riesz fractional derivative has been employed to describe the spatial derivative in a variety of mathematical models. In this work, the accuracy...
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Riesz Multiresolution Analysis on Locally Compact Abelian Groups: Construction and Exceptions
AbstractIn this article, we construct a Riesz multiresolution analysis (MRA) on locally compact Abelian groups (LCA) starting from a suitably given...
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ON BOUNDEDNESS OF THE GENERALIZED RIESZ POTENTIAL IN LOCAL MORREY-TYPE SPACES
For all admissible values of the numerical parameters sharp sufficient conditions on the functional parameters are obtained ensuring the boundedness...
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