Related papers: Closed form solution of non-homogeneous equations …

In this paper the linear non linear non homogenous integral equations of H- functions is considered to find a new form of H- function as its solution.The Wiener Hopf technique is used to express a known function into two functions with…

We prove variants of Wiener's Tauberian theorem in the framework of quantum harmonic analysis, i.e. for convolutions between an absolutely integrable function and a trace class operator, or of two trace class operators. Our results include…

Two variants of generalizations of Hankel operators to the case of linearly ordered abelian groups are considered, criteria of the boundedness and compactness of these operators are given, among them in terms of functions of bounded mean…

The existence of singularities of the solution for a class of Lax equations is investigated using a development of the fac- torization method first proposed by Semenov-Tian-Shansky and Reymann [11], [9]. It is shown that the existence of a…

Motivated by the Sarason problem on the products of Hankel and Toeplitz operators on analytic function spaces, we characterize the compactness of products of block Hankel and Toeplitz operators on the vector-valued Hardy space of the unit…

The purpose of this paper is to describe asymptotic formulas for determinants of a sum of finite Toeplitz and Hankel matrices with singular generating functions. The formulas are similar to those of the analogous problem for finite Toeplitz…

We extend results on compressed Toeplitz operators on the backward shift invariant subspaces of $H^2 $ to the context of the spaces $H^p$, $1<p<\infty.$

A Thue-Mahler equation is a Diophantine equation of the form $$F(X,Y) = a\cdot p_1^{z_1}\cdots p_v^{z_v}, \qquad \gcd(X,Y)=1$$ where $F$ be an irreducible homogeneous binary form of degree at least $3$ with integer coefficients, $a$ is a…

Let $a(z)=\sum_{i\in\mathbb Z}a_iz^i$ be a complex valued function defined for $|z|=1$, such that $\sum_{i\in\mathbb Z}|ia_i|<\infty$, and let $E=(e_{i,j})_{i,j\in\mathbb {Z}^+}$ be such that $\sum_{i,j\in\mathbb{Z}^+}|e_{i,j}|<\infty$. A…

We consider active scalar equations $\partial_t \theta + \nabla \cdot (u \, \theta) = 0$, where $u = T[\theta]$ is a divergence-free velocity field, and $T$ is a Fourier multiplier operator with symbol $m$. We prove that when $m$ is not an…

Motivated by Barr{\'\i}a-Halmos's \cite[Question 19]{barria1982asymptotic} and Halmos's \cite[Problem 237]{Halmos1978A}, we explore projections in Toeplitz algebra on the Hardy space. We show that the product of two Toeplitz (Hankel)…

In this paper, we deal with the following double phase problem $$ \left\{\begin{array}{ll} -\mbox{div}\left(|\nabla u|^{p-2}\nabla u+a(x)|\nabla u|^{q-2}\nabla u\right)=…

We consider Toeplitz operators defined on a concave corner-shaped subset of the square lattice. We obtain a necessary and sufficient condition for these operators to be Fredholm. We further construct a Fredholm concave corner Toeplitz…

Suppose $\mathcal{T}_{+}(E)$ is the tensor algebra of a $W^{*}$-correspondence $E$ and $H^{\infty}(E)$ is the associated Hardy algebra. We investigate the problem of extending completely contractive representations of $\mathcal{T}_{+}(E)$…

In this paper, we study Toeplitz operators with a positive symbol on pluriharmonic Fock spaces over $\mathbb{C}^{n}.$ We characterize the conditions under which the Toeplitz operator $T_\mu$ is bounded, compact, or belongs to the Schatten…

In this paper we introduce and study the class of weighted multi-Toeplitz operators associated with noncommutative polydomains ${\bf D_f^m}$, ${\bf m}:=(m_1,\ldots, m_k)\in {\bf N}^k$, generated by $k$-tuples ${\bf f}:=(f_1,\ldots, f_k)$ of…

The condition numbers $CN(T)==||T|| .||T^{-1}|| $ of Toeplitz and analytic $n\times n$ matrices $T$ are studied. It is shown that the supremum of $CN(T)$ over all such matrices with $||T|| \leq1$ and the given minimum of eigenvalues…

We prove that Toeplitz operators are norm dense in the Toeplitz algebra $\mathfrak{T}(L^\infty)$ over the weighted Bergman space $\mathcal{A}^2_\nu(\Omega)$ of a bounded symmetric domain $\Omega\subset\mathbb{C}^n$. Our methods use…

We consider an equation of the form $y'(t) + Ay(t) = 0, \ t \in [0, \infty)$, where $A$ is a nonnegative self-adjoint operator in a Hilbert space. We give direct and inverse theorems on approximation of solutions of this equation with its…

For $0<p\leq\infty$, let $F^{p}_\varphi$ be the Fock space induced by a weight function $\varphi$ satisfying $ dd^c \varphi \simeq \omega_0$. In this paper, given $p\in (0, 1]$ we introduce the concept of weakly localized operators on $…