Related papers: The truncated Fourier operator. II
The composition of the Fourier transform in $\mathbb{R}^n$ with a suitable pseudodifferential operator is called a Fourier operator. It is compact in appropriate function spaces. The paper deals with its spectral theory. This is based on…
The paper deals with a fractional derivative introduced by means of the Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve in complex plane is deduced and the…
In this paper we consider asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. We compute the dimension of the space of all such operators. We also describe the matrix representations of asymmetric…
Spectral properties of many finite convolution integral operators have been understood by finding differential operators that commute with them. In this paper we compile a complete list of such commuting pairs, extending previous work to…
We show that analytic pseudodifferential and Fourier integral operators behave well for ultradifferentiable classes satisfying minimal regularity properties. As an application we investigate the ultradifferentiable regularity properties of…
We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of…
In this paper we present some consequences of the description of matrix representations of asymmetric truncated Toeplitz operators acting between finite-dimensional model spaces. In particular, we prove that these operators can be…
Let $\theta$ be a non-constant inner function and let $\phi=\overline{u}v$, where $u$ and $v$ are inner functions such that $v$ divides $\theta$. In this paper we characterize the partially isometric truncated Toeplitz operators $A_{\phi}$…
In connection with the Fuglede conjecture, we study the existence of commuting self-adjoint extensions of the partial differential operators on arbitrary, possibly disconnected domains in $\br^d$, the associated unitary group, the spectral…
We consider first order linear operators commuting with the operator appearing in the linearized equation of motion of Rarita-Schwinger fields which comes directly from the action. First we consider a simplified operator giving an equation…
A triple of commuting operators for which the closed tetrablock $\overline{\mathbb E}$ is a spectral set is called a tetrablock contraction or an $\mathbb E$-contraction. The set $\mathbb E$ is defined as \[ \mathbb E = \{…
The $E_2$ term of the Adams spectral sequence may be identified with certain derived functors, and this also holds for a number of other spectral sequences. Our goal is to show how the higher terms of such spectral sequences are determined…
The aim of this paper is to investigate asymmetric truncated Toeplitz operators with $L^2$ symbols between two different model spaces given by inner functions such that one divides the other. Characterizations of these operators are given…
We study a commuting triple of bounded operators $(A, B, P)$ which has the tetrablock as a spectral set.
We study the geometry and partial differential equations arising from the consideration of group-determinants, and representation theory. The simplest and most striking such example is undoubtedly that of the Humbert operator, associated…
Parametric factorizations of linear partial operators on the plane are considered for operators of orders two, three and four. The operators are assumed to have a completely factorable symbol. It is proved that ``irreducible'' parametric…
Truncated Fourier Transforms (TFTs), first introduced by Van der Hoeven, refer to a family of algorithms that attempt to smooth "jumps" in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in…
We present two algorithms for computing what we call the absolute factorization of a difference operator. We also give an algorithm to solve third order difference equations in terms of second order equations, together with applications to…
We introduce the notion of the Dual Truncated Hankel Operator (DTHO) and provide several operator equation characterizations using the dual compressed shift operator. These characterizations are similar to classical results concerning…
Partial Fourier transforms are used to find explicit formulas for two remarkable fundamental solutions for a generalized Tricomi operator. These fundamental solutions reflect clearly the mixed type of the operator. In order to prove these…