Related papers: The index of singular integral operators with disc…

We construct an index of first-order, self-adjoint, elliptic differential operators in the $K$-theory of a Fr\'echet algebra of smooth kernels with faster than exponential off-diagonal decay. We show that this index can be represented by an…

We present an integral representation formula for a Dirichlet series whose coefficients are the values of the Liouville's arithmetic function.

In this paper, we shall prove the uniform sharp $L^p$ decay estimates for a class of oscillatory integral operators with polynomial phases. By this one-dimensional result, we can use the rotation method to obtain uniform sharp $L^p$…

We discuss Sekiguchi-type differential operators, their eigenvalues, and a generalization of Andrews-Goulden-Jackson formula. These will be applied to extract explicit formulae involving shifted partitions and hook lengths.

We study the Hp-Lq boundedness of certain integral operators of fractional type.

The article is devoted to the investigation of operators on a non locally compact group algebra. Their isomorphisms are also studied.

We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…

For entire operators and entire operators in the generalized sense, we provide characterizations based on the spectra of their selfadjoint extensions. In order to obtain these spectral characterizations, we discuss the representation of a…

The Dunkl operators associated to a dihedral group are a pair of differential-difference operators that generate a commutative algebra acting on differentiable functions in $\mathbb{R}^2$. The intertwining operator intertwines between this…

Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.

Applying perturbation theory methods, the absence of the point spectrum for some nonselfadjoint integro-differential operators is investigated. The considered differential operators are of arbitrary order and act in either…

A class of first order linear impulsive differential equation with continuous and piecewise constant arguments is studied. Sufficient conditions for the oscillation of the solutions are obtained.

For Dirac operators, which have discrete spectra, the concept of eigenvalues gradient is given and formulae for this gradients are obtained in terms of normalized eigenfunctions. It is shown how the gradient is being used to describe…

We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…

Callias-type (or Dirac-Schr\"odinger) operators associated to abstract semifinite spectral triples are introduced and their indices are computed in terms of an associated index pairing derived from the spectral triple. The result is then…

Bernoulli numbers are usually expressed in terms of their lower index numbers (recursive). This paper gives an explicit formula for Bernoulli numbers of even index. The formula contains a remarkable sequence of determinants.

We study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series, which we call the Wiener-Dirichlet algebra. The central issue is to understand the connection…

Real and imaginary part of the limit 2N->infinity of the integral int_{x=1..2N} exp(i*pi*x)*x^(1/x) dx are evaluated to 20 digits with brute force methods after multiple partial integration, or combining a standard Simpson integration over…

We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator Decomposition), which acts the…

The scaling limit and Schauder bounds are derived for a singular integral operator arising from a difference equation approach to monodromy problems.