Related papers: Riesz-Jacobi transforms as principal value integra…
Classical integral representation of the Mellin type kernel in terms of the Laplace integral gives an idea to construct a new class of non-convolution (index) transforms. Particular examples give the Kontorovich-Lebedev-like transformation…
We consider the problem of embedding eigenvalues into the essential spectrum of periodic Jacobi operators, using an oscillating, decreasing potential. To do this we employ a geometric method, previously used to embed eigenvalues into the…
The structured operators and corresponding operator identities, which appear in inverse problems for the self-adjoint and skew-self-adjoint Dirac systems with rectangular potentials, are studied in detail. In particular, it is shown that…
The spectral properties of two special classes of Jacobi operators are studied. For the first class represented by the $2M$-dimensional real Jacobi matrices whose entries are symmetric with respect to the secondary diagonal, a new…
By the Riesz representation theorem using the Riemann-Stieltjes integral, linear continuous functionals on the set of continuous functions from the unit interval into the reals can either be characterized by functions of bounded variation…
The explicit description and computation of functions defined on Riemann surfaces of various genera depends on the choice of language: while the Jacobi parametrization is widely known and used, the Schottky uniformization has been proven to…
There have been many proposed forms of fractional calculus, which can be grouped into a few broad classes of operators. By replacing the kernel of the power function with another kernel function, the traditional Riemann-Liouville formula…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
We establish several fundamental properties of one-sided (generalized) Drazin inverses in Banach algebras, including intertwining properties and reverse order laws. In particular, we introduce the concepts of one-sided strongly…
We study the behaviour of singular integral operators $T_{k_t}$ of convolution type on $\mathbb{C}$ associated with the parametric kernels $$ k_t(z):=\frac{(\Re z)^{3}}{|z|^{4}}+t\cdot \frac{\Re z}{|z|^{2}}, \quad t\in \mathbb{R},\qquad…
In this paper, Orlicz valuations compatible with $SL(n)$ transforms are classified. Unlike their $L_p$ analogs, the identity operator and the reflection operator are the only $SL(n)$ compatible Orlicz valuations (up to dilations). It turns…
We consider symmetric second-order differential operators with real coefficients such that the corresponding differential equation is in the limit circle case at infinity. Our goal is to construct the theory of self-adjoint realizations of…
We prove H\"older regularity for a general class of parabolic integro-differential equations, which (strictly) includes many previous results. We present a proof which avoids the use of a convex envelop as well as give a new covering…
We study the spectra of non-selfadjoint first-order operators on the interval with non-local point interactions, formally given by ${i\partial_x+V+k\langle \delta,\cdot\rangle}$. We give precise estimates on the location of the eigenvalues…
We introduce the notion of Ricci-corrected differentiation in parabolic geometry, which is a modification of covariant differentiation with better transformation properties. This enables us to simplify the explicit formulae for standard…
Analogous of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflection group. The $L^p$ boundedness of these operators is…
We describe a type of n-point function associated to strongly regular vertex operator algebras V and their irreducible modules. Transformation laws with respect to the Jacobi group are developed for 1-point functions. For certain elements…
We study a new class of pseudo differential operators whose symbols satisfy the differential inequality with a mixture of homogeneities. On the other hand, by taking singular integral realization, it can be equivalently defined by kernels…
We dominate non-integral singular operators by adapted sparse operators and derive optimal norm estimates in weighted spaces. Our assumptions on the operators are minimal and our result applies to an array of situations, whose prototype are…
This paper intends to construct discrete spectral transformations for Cauchy-Jacobi orthogonal polynomials, and find its corresponding discrete integrable systems. It turns out that the normalization factor of Cauchy-Jacobi orthogonal…