Related papers: The truncated Fourier operator. II
Truncated Toeplitz operators are compressions of Toeplitz operators on model spaces; they have received much attention in the last years. This survey article presents several recent results, which relate boundedness, compactness, and…
Partial transpose is an important operation for quantifying the entanglement, here we study the (partial) transpose of any single (two-mode) operators. Using the Fock-basis expansion, it is found that the transposed operator of an arbitrary…
We investigate second order elliptic equations \[F(\mathcal{H}u) = 0\] where the function $F\colon S(n)\to\mathbb{R}$ on the space of symmetric $n\times n$ matrices is assumed to be sublinear. There is very little to be found in the…
In this article, we describe the spectral sheaves of algebras of commuting differential operators of genus one and rank two with singular spectral curve, solving a problem posed by Previato and Wilson. We also classify all indecomposable…
Truncated Fourier, Gauss, Kummer and exponential sums can be used to factorize numbers: for a factor these sums equal unity in absolute value, whereas they nearly vanish for any other number. We show how this factorization algorithm can…
When Fourier series are used for applications in physics, involving partial differential equations, sometimes the process of resolution results in divergent series for some quantities. In this paper we argue that the use of linear low-pass…
The second order symmetry operators that commute with the Dirac operator with external vector, scalar and pseudo-scalar potentials are computed on a general two-dimensional spin-manifold. It is shown that the operator is defined in terms of…
This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient…
First, we consider generalized wave and scattering operators and derive modifications of commutation relations (between scattering operators and unperturbed operators) when the corresponding deviation factors behave as $\exp\{i t {\mathcal…
By means of a truncation condition on the parameters, the elliptic Ruijsenaars difference operators are restricted onto a finite lattice of points encoded by bounded partitions. A corresponding orthogonal basis of joint eigenfunctions is…
We investigate continuous linear operators, which commute with the generalized backward shift operator (a one-dimensional perturbation of the Pommiez operator) in a countable inductive limit $E$ of weighted Banach spaces of entire…
The classical Fourier transform on the line sends the operator of multiplication by $x$ to $i\frac{d}{d\xi}$ and the operator of differentiation $\frac{d}{d x}$ to the multiplication by $-i\xi$. For the Fourier transform on the Lobachevsky…
The Fourier transform of a bounded measurable function, $f$, on the real line is shown to be the second distributional derivative of a H\"older continuous function. The Fourier transform is written as the difference of $\int_{-1}^1…
Matrix valued (asymmetric) truncated Toeplitz operators are generally not complex symmetric. In this paper, we define a new conjugation with unique properties and study its relation to matrix valued asymmetric truncated Toeplitz operators.…
It is proved that given $-1/2<s<1/2$, for any $f\in L^2(\mathbb{R})$, there is a unique $u\in \widehat{H}^{|s|}(\mathbb{R})$ such that $$ f=\boldsymbol{D}^{-s}u+\boldsymbol{D}^{s*}u\,, $$ where $\boldsymbol{D}^{-s}, \boldsymbol{D}^{s*}$ are…
We propose a conceptual frame to interpret the prolate differential operator, which appears in Communication Theory, as an entropy operator; indeed, we write its expectation values as a sum of terms, each subject to an entropy reading by an…
In this note we introduce some nonlinear extremal nonlocal operators that approximate the, so called, truncated Laplacians. For these operators we construct representation formulas that lead to the construction of what, with an abuse of…
In this paper we study truncated moment problems for $J$-self-adjoint, $J$-skew-self-adjoint and $J$-unitary operators. Conditions of the solvability are given. Some canonical solutions of the moment problems are constructed. As a…
We indicate smooth real commuting matrix differential operators whose eigenvalues and eigenfunctions are parametrized by two-dimensional principally polarized abelian varieties.
Self-adjoint rank two commuting ordinary differential operators are studied in this paper. Such operators with trigonometric, elliptic and rapid decay coefficients corresponding to hyperelliptic spectral curves are constructed. Some…