Operators of Hardy type
Copyright policy )Operators of Hardy type
Among William Desmond Evans's many outstanding contributions to analysis, his work on operators of Hardy type plays a prominent role. Such an operator \(T\) is of the form \(Tf(x)=\upsilon(x)\int_a^x u(t)f(t)\,dt\), where \(u\) and \(\upsilon\) are given functions on an interval \((a,b)\) that satisfy certain integrability conditions, and \(T\) is viewed as a map between Lebesgue spaces. In this paper, the authors describe some of results concerning entropy and approximation numbers of operators of Hardy type in which Des Evans has played a major part, in the context of operators on intervals and on trees, and also mention some quite recent developments involving the Bernstein widths of \(T\) as well as its Kolmogorov widths and approximation numbers.
- Cardiff University United Kingdom
Integral operators, approximation numbers, Approximation numbers, Applied Mathematics, Approximation by arbitrary nonlinear expressions; widths and entropy, weighted Hardy-type operators, Bernstein and Kolmogorov widths, \(pq\)-Laplacian, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Kolmogorov width, Computational Mathematics, Bernstein width, Linear operators on function spaces (general), Weighted Hardy-type operators, pq-Laplacian, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
Integral operators, approximation numbers, Approximation numbers, Applied Mathematics, Approximation by arbitrary nonlinear expressions; widths and entropy, weighted Hardy-type operators, Bernstein and Kolmogorov widths, \(pq\)-Laplacian, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Kolmogorov width, Computational Mathematics, Bernstein width, Linear operators on function spaces (general), Weighted Hardy-type operators, pq-Laplacian, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
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