Related papers: A note on special duality triads and their operato…
We present new examples of complexes of differential operators of order $k$ (any given positive integer) that satisfy div-curl and/or $L^1$-duality estimates.
We establish a characterization of unitary equivalence of two bilateral operator valued weighted shifts with quasi-invertible weights by an operator of diagonal form. We also present an example of unitary equivalence between shifts defined…
This paper deals with eigenvalues and eigenvectors of bicomplex linear operators defined on bicomplex space. We investigate the properties of these operators in the context of eigenvalues and eigenvectors, along with some relevant theorems.…
Umbral extensions of the stirling numbers of the second kind are considered and the resulting dobinski-like various formulas including new ones are presented. These extensions naturally encompass the two well known q-extensions. The further…
An analysis of extension of Hamiltonian operators from lower order to higher order of matrix paves a way for constructing Hamiltonian pairs which may result in hereditary operators. Based on a specific choice of Hamiltonian operators of…
The operators of fractional calculus come in many different types, which can be categorised into general classes according to their nature and properties. We conduct a formal study of the class known as weighted fractional calculus and its…
New representation of the odderon wave function is derived, which is convergent in the whole impact parameter plane and provides the analytic form of the quantization condition for the integral of motion q_3. A new quantum number, triality,…
The extensions of the affine vertex operator algebras $L_{sl_2}(k,0)$ and the preunitary vertex operator algebras with central charges $c<1$ are classified. In particular, the unitary vertex operator algebras with central charges $c<1$ are…
We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and…
We construct an extension of the Kontsevich integral of knots to knotted trivalent graphs, which commutes with orientation switches, edge deletions, edge unzips, and connected sums. In 1997 Murakami and Ohtsuki [MO] first constructed such…
Creation operators are given for the three distinguished bases of the type BCD universal character ring of Koike and Terada yielding an elegant way of treating computations for all three types in a unified manner. Deformed versions of these…
We consider Tuenter polynomials as linear combinations of descending factorials and show that coefficients of these linear combinations are expressed via a Catalan triangle of numbers. We also describe a triangle of coefficients in terms of…
In this paper, extensions of nonunitary rational Virasoro vertex operator algebras corresponding to some exceptional modular invariants are constructed. The uniqueness of these extensions is also established.
Our objective in this paper is to introduce and investigate a newly-constructed subclass of normalized analytic and bi-univalent functions by means of the Chebyshev polynomials of the second kind. Upper bounds for the second and third…
In this paper we give some sufficient conditions of analyticity and univalence for functions defined by an integral operator. Next, we refine the result to a quasiconformal extension criterion with the help of the Becker's method. Further,…
We classify one-element extensions of a hyperplane arrangement by the induced adjoint arrangement. Based on the classification, several kinds of combinatorial invariants including Whitney polynomials, characteristic polynomials, Whitney…
Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…
We formulate the notion of equivariance of an operator with respect to a covariant representation of a C^*-dynamical system. We then use a combinatorial technique used by the authors earlier in characterizing spectral triples for SU_q(2) to…
This paper is in continuation of our work in \cite{PNM}, wherein we introduced generalized Baskakov Kantorovich operators $K_n^a(f;x)$ and established some approximation properties e.g. local approximation, weighted approximation,…
We introduce another new type of combinations of Bernstein operators in this paper, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type…