Related papers: On some systems of difference equations
In this article, by combining appropriate refined Bohr's inequalities with some techniques concerning bounded analytic functions defined in the unit disk, we generalize and improve several Bohr type inequalities for such functions.
The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…
Discrete analogs of the index transforms with squares of Bessel functions of the first and second kind $J_\nu(z),\ Y_\nu(z)$ are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and…
New index transforms, involving squares of Kelvin functions, are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The results are applied to solve a boundary value problem on…
We present a new method for proving Correa-Jofr\'e-Thibault theorem that monotonicity of subdifferential implies convexity of the function. This new method is based on barrier functions. Barrier functions help overcome some of the main…
In the first part we associate a periodic sequence to a partition and study the connection the distribution of elements of uniform limit of the sequences. Then some facts of statistical independence of these limits are proved
Different finite difference replacements for the derivative are analyzed in the context of the Heisenberg commutation relation. The type of the finite difference operator is shown to be tied to whether one can naturally consider $P$ and $X$…
We study the distribution of divisors of Euler's totient function and Carmichael's function. In particular, we estimate how often the values of these functions have "dense" divisors.
Boundary differentiability is shown for solutions of nondivergence elliptic equations with unbounded drift
Expressions for the derivatives with respect to order of modified Bessel functions evaluated at integer orders and certain integral representations of associated Legendre functions with modulus argument greater than unity are used to…
The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…
Using, as main tool, the convergence theorem for discrete martingales and the mean value property of harmonic functions we solve, a particular case of, Dirichlet problem.
We review the author's results on Mather's $\beta$ function : non-strict convexity of $\beta$ when the configuration space has dimension two, link between the size of the Aubry set and the differentiability of $\beta$, correlation between…
We investigate the interplay between linear systems on curves and graphs in the context of specialization of divisors on an arithmetic surface. We also provide some applications of our results to graph theory, arithmetic geometry, and…
This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…
Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of…
We survey the classical results of the Dirichlet Approximation Theorem.
We establish effective elimination theorems for differential-difference equations. Specifically, we find a computable function $B(r,s)$ of the natural number parameters $r$ and $s$ so that for any system of algebraic differential-difference…
The present article deals with properties of one class of functions with complicated local structure. These functions can be modeled by certain operators of digits. Such operators were considered by the author earlier (for example, see [27,…
This is a complement to my previous article "Advanced Determinant Calculus" (S\'eminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described…