Related papers: Some Rarita-Schwinger Type Operators
An important instance of Rota-Baxter algebras from their quantum field theory application is the ring of Laurent series with a suitable projection. We view the ring of Laurent series as a special case of generalized power series rings with…
As an abstraction and generalization of the integral operator in analysis, integral operators (known as Rota-Baxter operators of weight zero) on associative algebras and Lie algebras have played an important role in mathematics and physics.…
In this paper, algorithms are developed for computing the Stirling transform and the inverse Stirling transform; specifically, we investigate a class of sequences satisfying a two-term recurrence. We derive a general identity which…
In this work we develop a general procedure for constructing the recursion operators fro non-linear integrable equations admitting Lax representation. Svereal new examples are given. In particular we find the recursion operators for some…
For the inclusion problem involving two maximal monotone operators, under the metric subregularity of the composite operator, we derive the linear convergence of the generalized proximal point algorithm and several splitting algorithms,…
In this paper we present a systematic study of regular sequences of quasi-nonexpansive operators in Hilbert space. We are interested, in particular, in weakly, boundedly and linearly regular sequences of operators. We show that the type of…
For associative commutative algebras $A$ with Rota-Baxter operator $R$ identities of the algebra $AR=(A,\circ)$, where $a\circ b= aR(b),$ are found.
We present explicit formulae for Weber-Schafheitlin type integrals and give them an interpretation as the kernel of a physically relevant operator related to the hamiltonian of Aharanov and Bohm. In particular, we derive explicit formulae…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…
This is a survey article. We consider different problems in connection with the behavior of functions of operators under perturbations of operators. We deal with three classes of operators: unitary operators, self-adjoint operators, and…
This paper refines the main results from our previous study on sparse bounds of generalized commutators of multilinear fractional singular integral operators in \cite{CenSong2412}. The key improvements are: 1. We replace pointwise…
We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.
We consider generalizations of Dunkl's differential-difference operators associated with groups generated by reflections. The commutativity condition is equivalent to certain functional equations. These equations are solved in many cases.…
General first- and higher-order intertwining relations between non-stationary one-dimensional Schr\"odinger operators are introduced. For the first-order case it is shown that the intertwining relations imply some hidden symmetry which in…
In this paper, we explore the limiting weak-type behaviors of some integral operators including maximal operators, singular and fractional integral operators and maximal truncated singular integrals et al. Some optimal limiting weak-type…
We associate to an integral operator a discrete one which is conceptually simpler, and study the relations between them.
Starting with nonsymmetric global difference spherical functions, we define and calculate spinor (nonsymmetric) global q-Whittaker functions for arbitrary reduced root systems, which are reproducing kernels of the DAHA-Fourier transforms of…
In our previous work, we introduced a new class of bounded potentials of the one-dimensional Schr\"odinger operator on the real axis, and a corresponding family of solutions of the KdV hierarchy. These potentials, which we call primitive,…
We introduce a class of fractional Dirac type operators with time variable coefficients by means of a Witt basis, the Djrbashian-Caputo fractional derivative and the fractional Laplacian, both operators defined with respect to some given…
We consider equations arising from rational Lax representations. A general method to construct recursion operators for such equations is given. Several examples are given, including a degenerate bi-Hamiltonian system with a recursion…