相关论文: On Generalized Functions in Adelic Quantum Mechani…

Using the Weyl quantization we formulate one-dimensional adelic quantum mechanics, which unifies and treats ordinary and $p$-adic quantum mechanics on an equal footing. As an illustration the corresponding harmonic oscillator is considered.…

p-Adic and adelic generalization of ordinary quantum cosmology is considered. In [1], we have calculated p-adic wave functions for some minisuperspace cosmological models according to the "no-boundary" Hartle-Hawking proposal. In this…

We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstras P-function using two…

The Dirac delta function is widely used in many areas of physics and mathematics. Here we consider the generalization of a Dirac delta function to allow the use of complex arguments. We show that the properties of a generalized delta…

We use a form of lifted harmonic analysis to develop a two-dimensional adelic integral representation of the zeta functions of simple arithmetic surfaces. Manipulations of this integral then lead to an adelic interpretation of the so-called…

A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra(pseudo)metrics defined by sequences of…

On the basis of analysis on the adele ring of any algebraic numbers field (Tate's formula) a regularization for divergent adelic products of gamma- and beta-functions for all completions of this field are proposed, and corresponding…

We have shown that in some region where the Euler integral of the first kind diverges, the Euler formula defines a generalized function. The connected of this generalized function with the Dirac delta function is found.

A short proof of the generalized Riemann hypothesis (gRH in short) for zeta functions $\zeta_{k}$ of algebraic number fields $k$ - based on the Hecke's proof of the functional equation for $\zeta_{k}$ and the method of the proof of the…

We develop a new concept of quantum mechanics which is based on a generalized space-time and on an action vector space similar to it. Both spaces are provided by algebraic properties. This allows to calculate the Dirac matrixes and to…

We calculate the partition function of a harmonic oscillator with quasi-periodic boundary conditions using the zeta-function method. This work generalizes a previous one by Gibbons and contains the usual bosonic and fermionic oscillators as…

We define the adelic hypergeometric function of special Gaussian type by means of a tower of hypergeometric curves. This function takes values in an adelic completed group ring and interpolates all the hypergeometric functions of the same…

A new classification of real functions and other related real objects defined within a compact interval is proposed. The scope of the classification includes normal real functions and distributions in the sense of Schwartz, referred to…

We model generalized harmonic functions on rings of differential operators and complex function spaces. The differential operators in the second Weyl-algebra that commute with rotations are described and leads to a natural notion for such…

We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is…

We give a representation of the classical Riemann $\zeta$-function in the half plane $\Re s>0$ in terms of a Mellin transform involving the real part of the dilogarithm function with an argument on the unit circle (associated Clausen…

Alesker's theory of generalized valuations unifies smooth measures and constructible functions on real analytic manifolds, extending classical operations on functions and measures. Alesker showed that these operations agree with the…

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…

We carry out "Hecke summation" for the classical Eisenstein series $E_k$ in an adelic setting. The connection between classical and adelic functions is made by explicit calculations of local and global intertwining operators and Whittaker…

We describe a new infinite family of multi-parameter functional equations for the Rogers dilogarithm, generalizing Abel's and Euler's formulas. They are suggested by the Thermodynamic Bethe Ansatz approach to the Renormalization Group flow…