Related papers: On the regularity of generic Hausdorff-type transf…
We establish new operational formulae of Burchnall type for the complex disk polynomials (generalized Zernike polynomials). We then use them to derive some interesting identities involving these polynomials. In particular, we establish…
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
We introduce and study in a general setting the concept of homogeneity of an operator and, in particular, the notion of homogeneity of an integral operator. In the latter case, homogeneous kernels of such operators are also studied. The…
Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…
We establish the convergence of pseudospectra in Hausdorff distance for closed operators acting in different Hilbert spaces and converging in the generalised norm resolvent sense. As an assumption, we exclude the case that the limiting…
A definition of summability is put forward in the framework of general Carleman ultraholomorphic classes in sectors, so generalizing $k-$summability theory as developed by J.-P. Ramis. Departing from a strongly regular sequence of positive…
Usually such area of mathematics as differential equations acts as a consumer of results given by functional analysis. This article will give an example of the reverse interaction of these two fields of knowledge. Namely, the derivation and…
The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…
A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure.…
We study operators that are generalizations of the classical Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo fractional derivatives. A useful formula relating the generalized fractional derivatives is proved,…
In this paper we calculate some Generalized Selberg integrals. The answer is expressed in terms of $\Gamma$-functions. Integrals of this type serve as normalization constants or directly via undoing 2-D integrals for determination of…
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
We introduce a deformation of the Fourier transform on $\mathbb{R}^N$ arising from a representation-theoretic construction associated with $\widetilde{SL}(2,\mathbb{R}) \times O(N)$ that still admits an underlying degree-one operator…
By means of the derivative operator and Whipple-type $_3F_2$-series identities, two families of summation formulae involving generalized harmonic numbers are established.
In the first part of this paper, we express the generalized Bessel function associated with dihedral systems and a constant multiplicity function as a infinite series of confluent Horn functions. The key ingredient leading to this…
A generalization of driven harmonic oscillator with time-dependent mass and frequency, by adding total time-derivative terms to the Lagrangian, is considered. The generalization which gives a general quadratic Hamiltonian system does not…
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
Integral operators of Abel type of order a > 0 arise naturally in a large spectrum of physical processes. Their inversion requires care since the resulting inverse problem is ill-posed. The purpose of this work is to devise and analyse a…
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…