Riesz bases of normalized reproducing kernels in Fock type spaces

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
K. P. Isaev ◽  
R. S. Yulmukhametov
Keyword(s):  
Reproducing Kernels ◽  
Riesz Bases ◽  
Type Spaces

Fock type spaces with Riesz bases of reproducing kernels and de Branges spaces

2017 ◽  
Vol 236 (2) ◽  
pp. 127-142 ◽  
Author(s):  
Anton Baranov ◽  
Yurii Belov ◽  
Alexander Borichev
Keyword(s):  
Reproducing Kernels ◽  
Riesz Bases ◽  
De Branges Spaces ◽  
Type Spaces

scholarly journals Riesz bases of reproducing kernels in Fock-type spaces

2009 ◽  
Vol 9 (3) ◽  
pp. 449-461 ◽  
Author(s):  
Alexander Borichev ◽  
Yurii Lyubarskii
Keyword(s):  
Reproducing Kernels ◽  
Riesz Bases ◽  
Fock Spaces ◽  
Type Spaces

AbstractIn a scale of Fock spaces $\mathcal{F}_\varphi$ with radial weights ϕ we study the existence of Riesz bases of (normalized) reproducing kernels. We prove that these spaces possess such bases if and only if ϕ(x) grows at most like (log x)2.

scholarly journals Sobolev-Type Spaces on the Dual of the Chébli-Trimèche Hypergroup and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Mourad Jelassi ◽  
Hatem Mejjaoli
Keyword(s):  
Differential Operator ◽  
Type Theorem ◽  
Reproducing Kernels ◽  
Second Order ◽  
Order Differential Operator ◽  
Sobolev Type ◽  
Weierstrass Transform ◽  
Sobolev Type Spaces ◽  
Type Spaces

We define and study Sobolev-type spacesWAs,pℝ+associated with singular second-order differential operator on0,∞. Some properties are given; in particular we establish a compactness-type imbedding result which allows a Reillich-type theorem. Next, we introduce a generalized Weierstrass transform and, using the theory of reproducing kernels, some applications are given.

scholarly journals Volterra operators on Hardy spaces of Dirichlet series

2019 ◽  
Vol 2019 (754) ◽  
pp. 179-223 ◽  
Author(s):  
Ole Fredrik Brevig ◽  
Karl-Mikael Perfekt ◽  
Kristian Seip
Keyword(s):  
Dirichlet Series ◽  
Carleson Measure ◽  
Volterra Operator ◽  
Bounded Operator ◽  
Reproducing Kernels ◽  
Coefficient Estimates ◽  
Volterra Operators ◽  
Type Spaces ◽  
Formula Type

Abstract For a Dirichlet series symbol {g(s)=\sum_{n\geq 1}b_{n}n^{-s}} , the associated Volterra operator {\mathbf{T}_{g}} acting on a Dirichlet series {f(s)=\sum_{n\geq 1}a_{n}n^{-s}} is defined by the integral {f\mapsto-\int_{s}^{+\infty}f(w)g^{\prime}(w)\,dw}. We show that {\mathbf{T}_{g}} is a bounded operator on the Hardy space {\mathcal{H}^{p}} of Dirichlet series with {0<p<\infty} if and only if the symbol g satisfies a Carleson measure condition. When appropriately restricted to one complex variable, our condition coincides with the standard Carleson measure characterization of {{\operatorname{BMOA}}(\mathbb{D})} . A further analogy with classical {{\operatorname{BMO}}} is that {\exp(c|g|)} is integrable (on the infinite polytorus) for some {c>0} whenever {\mathbf{T}_{g}} is bounded. In particular, such g belong to {\mathcal{H}^{p}} for every {p<\infty} . We relate the boundedness of {\mathbf{T}_{g}} to several other {{\operatorname{BMO}}} -type spaces: {{\operatorname{BMOA}}} in half-planes, the dual of {\mathcal{H}^{1}} , and the space of symbols of bounded Hankel forms. Moreover, we study symbols whose coefficients enjoy a multiplicative structure and obtain coefficient estimates for m-homogeneous symbols as well as for general symbols. Finally, we consider the action of {\mathbf{T}_{g}} on reproducing kernels for appropriate sequences of subspaces of {\mathcal{H}^{2}} . Our proofs employ function and operator theoretic techniques in one and several variables; a variety of number theoretic arguments are used throughout the paper in our study of special classes of symbols g.

Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2877-2889 ◽  
Author(s):  
Amir Sanatpour ◽  
Mostafa Hassanlou
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Essential Norm ◽  
Necessary And Sufficient Conditions ◽  
Norm Estimates ◽  
Type Spaces ◽  
Necessary And Sufficient

We study boundedness of weighted differentiation composition operators Dk?,u between Zygmund type spaces Z? and Bloch type spaces ?. We also give essential norm estimates of such operators in different cases of k ? N and 0 < ?,? < ?. Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.

scholarly journals Improving KKM Theory on General Metric Type Spaces

2021 ◽  
Vol 9 (1) ◽  
pp. 1-12
Author(s):  
Sehie Park
Keyword(s):  
Convex Space ◽  
Metric Spaces ◽  
Space Theory ◽  
Type Space ◽  
Generalized Metric ◽  
Abstract Convex Space ◽  
Type Spaces

Abstract A generalized metric type space is a generic name for various spaces similar to hyperconvex metric spaces or extensions of them. The purpose of this article is to introduce some KKM theoretic works on generalized metric type spaces and to show that they can be improved according to our abstract convex space theory. Most of these works are chosen on the basis that they can be improved by following our theory. Actually, we introduce abstracts of each work or some contents, and add some comments showing how to improve them.

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