Ramiz Tapdigoglu

Azerbaijan State University of Economics | UNEC · Department of Economics

Let \(\mathbb {A}\) be the \(2\times 2\) diagonal operator matrix determined by a positive Hilbert space operator A. We give several upper bounds for the \(\mathbb {A}\)-Berezin number of \(2\times 2\) block matrices on a reproducing kernel Hilbert space and prove inequalities for the A-Berezin number of Hilbert space operators. Our results in this...

We study some problems of operator theory by using Berezin symbols approach. Namely, we investigate in terms of Berezin symbols invariant subspaces of isometric composition operators on \({\mathcal {H}}\left( \Omega \right) .\) We discuss operator corona problem, in particular, the Toeplitz corona problem. Further, we characterize unitary operators...

We consider the Riccati operator equations on the weighted Bergman space A2? (Bn) of the unit ball Bn in Cn and investigate the properties of their solutions. Our discussion uses the Berezin symbols method.

We consider the space \(C^{\left( n\right) }\left( \Omega \right) ,\) the Banach space of continuous functions with n derivatives and the n th derivative continuous in \({\overline{\Omega }},\) where \(\Omega \subset {\mathbb {C}}\) is a starlike region with respect to \(\alpha \in \Omega .\) We use the so-called \(\alpha\)-Duhamel product $$\begin...

Let 𝔻 = { z ∈ C : | z | < 1} be the unit disk and Hol(𝔻 × 𝔻) be the space of all holomorphic functions on the bi-disc 𝔻 × 𝔻. We consider the double convolution operator 𝒦 f on the subspace Hol zw (𝔻 × 𝔻) := { f ∈ Hol(𝔻 × 𝔻) : f ( z,w ) = g ( zw ) for some g ∈ Hol(𝔻)} defined by K f h ( z w ) = ( f ∗ h ) ( z w ) := ∫ 0 z ∫ 0 w f ( ( z − u ) ( w − v...

We give some applications of Berezin transforms and Engliś C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^{*} $$\end{document}-algebras methods, namely we investig...

Let ? be a fixed complex number, and let ? be a simply connected region in complex plane C that is starlike with respect to ? ? ?. We define some Banach space of analytic functions on ? and prove that it is a Banach algebra with respect to the ?-Duhamel product defined by (f?? g)(z) := d/dz z?? f(z+??t)g(t)dt. We prove that its maximal ideal space...

We consider the Duhamel equation ? ? f = g in the subspace C? xy = {f ? C? ([0, 1] ? [0, 1]) : f (x, y) = F (xy) for some F ? C? [0, 1] of the space C? ([0, 1] ? [0, 1]) and prove that if ? pxy=0, 0, then this equation is uniquely solvable in C? x y. The commutant of the restricted double integration operator Wxy f (xy) := ?x 0 ?y 0 f (t?) d?dt on...

We use Kittaneh and Manasrah inequality and Kian’s functional calculus method to prove some new inequalities for Berezin symbols and Berezin numbers of operators. In particular, we prove that ( ber f (A)²⁾ (f(A) p ≥ ber +f )(A)q p q for all self-adjoint operators A on the reproducing kernel Hilbert space H (Ω) with spectrum in J ⊂ (−∞,+∞) and all c...

The Duhamel product for two suitable functions f and g is defined as follows: $$\begin{aligned} (f\circledast g)(x)={\frac{\mathrm{{d}}}{\mathrm{d}x}} {\textstyle \int \limits _{0}^{x}} f(x-t)g(t)\mathrm{{d}}t. \end{aligned}$$We consider the integration operator J, \(Jf(x)={\textstyle \int \limits _{0}^{x}} f(t)\mathrm{{d}}t\), on the Frechet space...

A time-fractional space-nonlocal reaction-diffusion equation in a bounded domain is considered. First, the existence of a unique local mild solution is proved. Applying Poincaré inequality it is obtained the existence and boundedness of global classical solution for small initial data. Under some conditions on the initial data, we show that solutio...

Let C .n/ D C .n/ .D D/ be a Banach space of complex valued functions f .x; y/ that are continuous on the closed bidisc D D, where D D ¹z 2 C W jzj < 1º is the unit disc in the complex plane C and has nth partial derivatives in D D which can be extended to functions continuous on D D. The Duhamel product is defined on C .n/ by the formula .f~g/.z;...

In this thesis, we are interested in solving some inverse problems for fractional differential equations. An inverse problem is usually ill-posed. The concept of an ill-posed problem is not new. While there is no universal formal definition for inverse problems, Hadamard [1923] defined a problem as being ill-posed if it violates the criteria of a w...

In this paper, we consider a non-linear sequential differential equation with Caputo fractional derivative of Blasius type and we reduce the problem to the equivalent non-linear integral equation. We prove the complete continuity of the non-linear integral operator. The theorem on the existence of a solution of the problem for the Blasius equation...

A class of inverse problems for restoring the right-hand side of a fractional heat equation with involution is considered. The results on existence and uniqueness of solutions of these problems are presented.

We consider an inverse problem for a space and time fractional evolution equation, interpolating the heat and wave equations, with an involution. Existence and uniqueness results for the given problem are obtained via the method of separation of variables.

We study the unicellularity problem for the Volterra integration operator f ! xR0 f (t) dt for the space C(n) [0; 1] of n times continuously differentiable functions on the unit segment [0; 1]. By applying Duhamel product technique an alternative proof of the Ostapenko-Tarasov theorem is given.

Using some general arguments, including the Duhamel product and its some modification, we describe all invariant subspaces of the Volterra integration operator V:f→∫0xf(t)dt and prove its unicellularity in more general Banach spaces of smooth functions on the unit segment [0,1][0,1].