Related papers: New Exponential operators connected with a^2+x^2: …
In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and quasiperiodic boundary conditions. Then using these…
The aim of this paper is to develop an approach to obtain self-adjoint extensions of symmetric operators acting on anti-dual pairs. The main advantage of such a result is that it can be applied for structures not carrying a Hilbert space…
We derive an asymptotic expansion analogous to the Hadamard expansion for powers of advanced/retarded Green's operators associated to a normally hyperbolic operator $P$, as well as expansions for advanced/retarded Green's operators…
Resolvent compositions were recently introduced as monotonicity-preserving operations that combine a set-valued monotone operator and a bounded linear operator. They generalize in particular the notion of a resolvent average. We analyze the…
We obtain Taylor approximations for functionals $V\mapsto Tr(f(H_0+V))$ defined on the bounded self-adjoint operators, where $H_0$ is a self-adjoint operator with compact resolvent and $f$ is a sufficiently nice scalar function, relaxing…
We obtain several sharp lower and upper bounds for the Euclidean operator radius of a pair of bounded linear operators defined on a complex Hilbert space. As applications of these bounds we deduce a chain of new bounds for the classical…
The indefinite Sturm-Liouville operator $A = (\sgn x)(-d^2/dx^2+q(x))$ is studied. It is proved that similarity of $A$ to a selfadjoint operator is equivalent to integral estimates of Cauchy integrals. Also similarity conditions in terms of…
An asymmetric operator of generalised translation is introduced in this paper. Using this operator, we define a generalised modulus of smoothness and prove direct and inverse theorems of approximation theory for it.
In this paper, we construct a linear positive operators q-parametric Szasz-Mirakjan operators generated by the q-Dunkl generalization of the exponential function. We obtain Korovkin's type approximation theorem for these operators and…
The exponential rate of convergence for some Markov operators is established. The operators correspond to continuous iterated function systems which are a very useful tool in some cell cycle models.
The sharp Gevrey hypoellipticity is provided for the following generalization of the M\'etivier operator, "Non-hypoellipticit\'e analytique pour $D_{x}^{2}+\left( x^{2} + y^{2}\right)D_{y}^{2}$" by G. M\'etivier, \begin{align*}…
The present paper aims to generalize the Schauder estimate for a class of higher-order hypo-elliptic operators. The results in the present paper apply to parabolic equations of higher order and, for example, operators like…
We study the vertical and conical square functions defined via elliptic operators in divergence form. In general, vertical and conical square functions are equivalent operators just in $L^2$. But when this square functions are defined…
The Schrodinger equations which are exactly solvable in terms of associated special functions are directly related to some self-adjoint operators defined in the theory of hypergeometric type equations. The fundamental formulae occurring in…
We study operators on a singular manifold, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. The idea is to construct so-called…
This paper is concerned with the asymptotic expansions of the amplitude of the solution of the Helmholtz equation. The original expansions were obtained using a pseudo-differential decomposition of the Dirichlet to Neumann operator. This…
Various formulas for reciprocals of densely defined weighted composition operators in $L^2$-spaces as well as for their adjoints are provided. The relation between the reciprocal of a weighted composition operator and the product of the…
Orthogonal polynomials $P_{n}(\lambda)$ are oscillating functions of $n$ as $n\to\infty$ for $\lambda$ in the absolutely continuous spectrum of the corresponding Jacobi operator $J$. We show that, irrespective of any specific assumptions on…
Within the framework of a manifestly gauge invariant exact renormalization group for SU(N) Yang-Mills, we derive a simple expression for the expectation value of an arbitrary gauge invariant operator. We illustrate the use of this formula…
A fast approximation to the Boys functions (related to the lower incomplete gamma function of half-integer parameter) by a single closed-form analytical expression for all argument values have been developed and tested. Besides the…