相关论文: Cohomology and Bessel functions Theory
Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…
The moments of Bessel functions and Bessel-trigonometric functions play a basic role in many practical problems and numerical analysis. This paper presents a complete analysis for these moments based on the recursive relations of Bessel…
We have solved a number of holonomic PDEs derived from the Bessel modules which are related to the generating functions of classical Bessel functions and the difference Bessel functions recently discovered by Bohner and Cuchta. This…
A new computational procedure is offered to provide simple, accurate and flexible methods for using modern computers to give numerical evaluations of the various Bessel functions. The Trapezoidal Rule, applied to suitable integral…
We reconsider quantum mechanical systems based on the classical action being the period of a one form over a cycle and elucidate three main points. First we show that the prepotenial V is no longer completely arbitrary but obeys a…
We develop a theory of bounded variation functions and Besov spaces in abstract Dirichlet spaces which unifies several known examples and applies to new situations, including fractals.
Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.
The survey is devoted to diverse applications of Besov classes in operator theory. It is illustrated how Besov classes are used to describe Hankel operators of Schatten--von Neumann classes; various applications of this description are…
Considering the kernel of an integral operator intertwining two realizations of the group of motions of the pseudo-Euclidian space, we derive two formulas for series containing Whittaker's functions or Weber's parabolic cylinder functions.…
Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…
It is shown that correlations of dichotomic functions can not conform to results from Quantum Mechanics. Also, it is seen that the assumptions attendant to optical tests of Bell's Inequalities actually are consistent with classical physics…
Modules for sesquiads and congruence schemes are introduced. It is shown that the corresponding categories are belian and that base change functors establish an ascent datum which allows for a cohomology theory to be established.
We prove explicit uniform two-sided bounds for the phase functions of Bessel functions and of their derivatives. As a consequence, we obtain new enclosures for the zeros of Bessel functions and their derivatives in terms of inverse values…
In the theory of configuration spaces, "splitting" usually refers to the phenomenon that the configuration spaces on a manifold and those on its punctured version are closely related cohomologically. We prove a splitting theorem that is…
The aim of this paper is to prove a trace theorem for Besov functions in the metric setting, generalizing a known result from A. Jonsson and H. Wallin in the Euclidean case. We show that the trace of a Besov space defined in a `big set' $X$…
We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the…
In a recent paper we investigated the internal space of Bessel functions associated with their orders. We found a formula (new) unifying Bessel functions of integer and of real orders. In this paper we study the deformed exterior derivative…
After proving the equivalence of the Bessel $K$-functional and the corresponding spherical modulus of smoothness we define fractional Bessel-Sobolev spaces. As an analog of the classical one the imbedding relation of fractional…
We consider the classical Besov and Triebel-Lizorkin spaces defined via differences and prove a homogeneity property for functions with bounded support in the frame of these spaces. As the proof is based on compact embeddings between the…
Similar to the associated Legendre functions, the differential equation for the associated Bessel functions $B_{l,m}(x)$ is introduced so that its form remains invariant under the transformation $l\rightarrow -l-1$. A Rodrigues formula for…