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F\'elix and Thomas extended the loop products and coproducts to simply-connected Gorenstein spaces. We explicitly describe these operations with rational coefficients in terms of Sullivan models. Moreover, by this description, we prove some…
Explicit expressions are given for the actions and radial matrix elements of basic radial observables on multi-dimensional spaces in a continuous sequence of orthonormal bases for unitary SU(1,1) irreps. Explicit expressions are also given…
We prove a realization theorem for rational functions of several complex variables which extends the main theorem of M. Bessmertnyi, "On realizations of rational matrix functions of several complex variables," in Vol. 134 of Oper. Theory…
The method of Taylor series expansion is used to develop a numerical solution to the reactor point kinetics equations. It is shown that taking a first order expansion of the neutron density and precursor concentrations at each time step…
Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are…
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The classical Hahn-Banach theorem is based on a successive point-by-point procedure of extending bounded linear functionals. In the setting of a general metric domain, the conditions are less restrictive and the extension is only required…
We consider the discrete analogue of a fractional integral operator on the Heisenberg group, for which we are able to prove nearly sharp results by means of a simple argument of a combinatorial nature.
In our recent publication we obtained a series expansion of the arctangent function involving complex numbers. In this work we show that this formula can also be expressed as a real rational function.
We calculate the effect of simple Hecke operators on u-expansions of higher rank Drinfeld modular forms, the eigenvalue for the Drinfeld discriminant function $\Delta_t$ and show that a certain natural class of Hecke operators is completely…
We introduce a new matrix model representation for the generating function of simple Hurwitz numbers. We calculate the spectral curve of the model and the associated symplectic invariants developed in [Eynard-Orantin]. As an application, we…
We relate a universal formula for the deformation quantization of arbitrary Poisson structures proposed by Maxim Kontsevich to the Campbell-Baker-Hausdorff formula. Our basic thesis is that exponentiating a suitable deformation of the…
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We establish nontrivial bounds for general bilinear forms with a given periodic function, which are thought of as an analogue of van der Corput differencing for exponential sums. The proof employs Poisson summation, Cauchy-Schwarz, and the…
These notes are an expanded version of a talk given by the second author. Our main interest is focused on the challenging problem of computing Kronecker coefficients. We decided, at the beginning, to take a very general approach to the…
The general Poisson summation formula of harmonic analysis and analytic number theory can be regarded as a quadrature formula with remainder. The purpose of this investigation is to give estimates for this remainder based on the classical…
The partial fraction expansion of coth($\pi$z), due to Euler, is generalized to power series having for coefficients the Riemann zeta function evaluated at certain arithmetic sequences. A further generalization using arbitrary Dirichlet…
The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…
We transformed the generalized exponential power series to another functional form suitable for further analysis. By applying the Cauchy-Euler differential operator in the form of an exponential operator, the series became a sum of…
One can introduce so-called {\em Plain Mechanics} having an {\bf operator realization}. Then the set of one-dimension representations of this operator realization may be identified with the Classical Mechanics. Different irreducible…