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Basic relations valid for the Bernstein spaces B ² σ and their extensions to larger function spaces via a unified distance concept

P. L. Butzer, R. L. Stens, G. Schmeisser (2014)

Banach Center Publications

Some basic theorems and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces B σ p are no longer valid in larger spaces. However, when a function f is in some sense close to a Bernstein space, then the corresponding relation holds with a remainder or error term. This paper presents a new, unified approach to these errors in terms of the distance of f from B σ p . The difficult situation of derivative-free error estimates is also covered.

Berezin and Berezin-Toeplitz quantizations for general function spaces.

Miroslav Englis (2006)

Revista Matemática Complutense

The standard Berezin and Berezin-Toeplitz quantizations on a Kähler manifold are based on operator symbols and on Toeplitz operators, respectively, on weighted L2-spaces of holomorphic functions (weighted Bergman spaces). In both cases, the construction basically uses only the fact that these spaces have a reproducing kernel. We explore the possibilities of using other function spaces with reproducing kernels instead, such as L2-spaces of harmonic functions, Sobolev spaces, Sobolev spaces of holomorphic...

Besov spaces and 2-summing operators

M. A. Fugarolas (2004)

Colloquium Mathematicae

Let Π₂ be the operator ideal of all absolutely 2-summing operators and let I m be the identity map of the m-dimensional linear space. We first establish upper estimates for some mixing norms of I m . Employing these estimates, we study the embedding operators between Besov function spaces as mixing operators. The result obtained is applied to give sufficient conditions under which certain kinds of integral operators, acting on a Besov function space, belong to Π₂; in this context, we also consider the...

Besov spaces and function series on Lie groups

Leszek Skrzypczak (1993)

Commentationes Mathematicae Universitatis Carolinae

In the paper we investigate the absolute convergence in the sup-norm of Harish-Chandra's Fourier series of functions belonging to Besov spaces defined on non-compact connected Lie groups.

Besov spaces and function series on Lie groups (II).

Leszek Skrzypczak (1993)

Collectanea Mathematica

In this paper we investigate the absolute convergence in the sup-norm of two-sided Harish-Chandra's Fourier series of functions belonging to Zygmund-Hölder spaces defined on non-compact connected Lie groups.[Part I of the article in MR1240211].

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