Banach Journal of Mathematical Analysis
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Linear prediction and simultaneous approximation by m-th order Kantorovich type sampling series
Banach Journal of Mathematical Analysis - Tập 14 - Trang 1481-1508 - 2020
In the present paper, a new family of sampling type operators is introduced and
studied. By the composition of the well-known generalized sampling operators of
P.L. Butzer with the usual differential and anti-differential operators of order
m, we obtain the so-called m-th order Kantorovich type sampling series. This
family of approximation operators are very general and include, as special
cases, ...
Davis–Wielandt shells of semi-Hilbertian space operators and its applications
Banach Journal of Mathematical Analysis - - 2020
Characterizations of generalized pencils of pairs of projections
Banach Journal of Mathematical Analysis - Tập 18 - Trang 1-19 - 2024
Let T be a bounded linear operator on a complex Hilbert space $$\mathcal {H}$$ .
We present some necessary and sufficient conditions for T to be the generalized
pencil $$P + \alpha Q +\beta PQ$$ of a pair (P, Q) of projections at some point
$$(\alpha , \beta )\in \mathbb {C}^2$$ . The range and kernel relations of the
generalized pencil T are studied and comments on the additional properties of
so...
On the classes of functions of generalized bounded variation
Banach Journal of Mathematical Analysis - Tập 14 - Trang 762-783 - 2020
The properties of the class of functions of generalized bounded variation are
studied. The “anomaly” feature of this class is revealed. There is the notation
of absolute continuity with respect to $$((p_n), \phi )$$ and it’s connection
with the ordinary absolute continuity is investigated. The problems of
approximation by Steklov’s functions and singular integrals are studied.
Localization operators on discrete modulation spaces
Banach Journal of Mathematical Analysis - Tập 17 - Trang 1-28 - 2023
In this paper, we study a class of pseudo-differential operators known as
time-frequency localization operators on $${\mathbb {Z}}^n$$ , which depend on a
symbol $$\varsigma $$ and two windows functions $$g_1$$ and $$g_2$$ . We define
the short-time Fourier transform on $$ {\mathbb {Z}}^n \times {\mathbb {T}}^n $$
and modulation spaces on $${\mathbb {Z}}^n$$ , and present some basic
properties. Th...
The core operator and the compressed multipliers on $$M_{\psi ,\varphi }$$ -type submodules
Banach Journal of Mathematical Analysis - Tập 16 - Trang 1-23 - 2022
Structure of submodules in $$H^{2}({\mathbb {D}}^{2})$$ is very complicated. A
good understanding of some special examples will shed light on the general
picture. This paper studies the submodule $$M_{\psi ,\varphi }=[\psi (z)-\varphi
(w)]$$ and the corresponding quotient module $$N_{\psi ,\varphi }=H^{2}({\mathbb
{D}}^{2})\ominus M_{\psi ,\varphi }$$ . This paper calculates the
Hilbert–Schmidt no...
Carleson measures and Berezin-type operators on Fock spaces
Banach Journal of Mathematical Analysis - - 2024
We characterize (vanishing) Fock–Carleson measures by products of functions in
Fock spaces. We also study the boundedness of Berezin-type operators from a
weighted Fock space to a Lebesgue space. Due to the special properties of
Fock–Carleson measures, the boundedness of Berezin-type operators on Fock spaces
is different from the corresponding results on Bergman spaces.
Equality in Hausdorff–Young for hypergroups
Banach Journal of Mathematical Analysis - Tập 16 - Trang 1-31 - 2022
It was shown in [Colloq. Math. 131(2), 219--231 (2013)] that one can extend the
domain of Fourier transform of a commutative hypergroup K to $$L^p(K)$$ for
$$1\le p \le 2$$ , and the Hausdorff–Young inequality holds true for these
cases. In this article, we examine the structure of non-zero functions in
$$L^p(K)$$ for which equality is attained in the Hausdorff–Young inequality, for
$$1...
An extension of the a-numerical radius on $$C^*$$ -algebras
Banach Journal of Mathematical Analysis - Tập 17 - Trang 1-23 - 2023
Let a be a positive element in a unital $$C^*$$ -algebra $$\mathfrak {A}$$ . We
define a semi-norm on $$\mathfrak {A}$$ , which generalizes the a-operator
semi-norm and the a-numerical radius. We investigate the basic properties of
this semi-norm and prove inequalities involving it. Further, we derive new upper
and lower bounds for the a-numerical radii of elements in $$\mathfrak {A}$$ .
Some othe...
Dual spaces for variable martingale Lorentz–Hardy spaces
Banach Journal of Mathematical Analysis - Tập 15 - Trang 1-31 - 2021
Let $$H_{p(\cdot ),q}$$ be the variable Lorentz–Hardy martingale spaces. In this
paper, we give a new atomic decomposition for these spaces via simple $$L_r$$
-atoms $$(1...
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