Related papers: Cauchy Integral Formula for Fuchsian Groups. II

We give a few properties equivalent to the Bloch-Kato conjecture (now the norm residue isomorphism theorem).

In this work we define operator-valued Fourier transforms for suitable integrable elements with respect to the Plancherel weight of a (not necessarily Abelian) locally compact group. Our main result is a generalized version of the Fourier…

We formulate and prove an analogue of Beurling's theorem for the Fourier transform on the Heisenberg group. As a consequence we deduce Hardy and Cowling-Price theorems.

We introduce Nakayama functors for coalgebras and investigate their basic properties. These functors are expressed by certain (co)ends as in the finite case discussed by Fuchs, Schaumann, and Schweigert. This observation allows us to define…

We consider a one-parameter family of functions $\{F(t,x)\}_{t}$ on $[0,1]$ and partial derivatives $\partial_{t}^{k} F(t, x)$ with respect to the parameter $t$. Each function of the class is defined by a certain pair of two square matrices…

The purpose of this paper is to present a generalization of Forelli's theorem. In particular, we prove an all dimensional version of the two-dimensional theorem of Chirka of 2005.

This study is on Cauchy's function $f(z)$ and its integral, $J[f(z)]\equiv (2\pi i)^{-1}\oint_C f(t)dt/(t-z)$ taken along a closed simple contour $C$, in regard to their comprehensive properties over the entire $z=x+iy$ plane consisted of…

In this note a generalization of the Lamb-Bateman integral equation is presented and its solution is given in terms of {\bf fractional derivatives}. This is a comment one to the paper by Babusci, Dattoli and Sacchetti (arXiv:1006.0184…

We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.

In this work derivations of definite integrals listed in Prudnikov volume I, Gradshteyn and Ryzhik and a few other tables are produced. Special cases of these integrals in terms of fundamental constants are also evaluated. The method used…

The universal method of expansion of integrals is suggested. It allows in particular to derive the threshold expansion of Feynman integrals.

We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group $H \leq \mathrm{SL}(n,…

In this note a general a Cauchy-type mean value theorem for the ratio of functional determinants is offered. It generalizes Cauchy's and Taylor's mean value theorems as well as other classical mean value theorems.

In this paper we obtain a generalization of some integral inequalities related to Chebyshev`s functional by using a generalized Katugampola fractional integral.

We prove three sharp estimates for the generalized Zalcman coefficient functional: one for the Hurwitz class, another for the Noshiro-Warschawski class, and yet another for the functions in the closed convex hull of convex univalent…

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.

This is the revised version of the second paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. The theory will be illustrated in upcoming papers by applications to Floer Theory,…

We extend Gromov's notion of asymptotic dimension of finitely generated groups to all discrete groups. In particular, we extend the Hurewicz type theorem proven in [B-D2] to general groups. Then we use this extension to prove a formula for…

This article contains a new discussion for the generalized fractional Cauchy-type problem involving Hilfer-Katugampola-type fractional derivative. We study an existence and continuation of its solution. Firstly, we establish a new theorems…

In this announcement we generalize the Markov-Kakutani fixed point theorem for abelian semi-groups of affine transformations extending it on some class of non-commutative semi-groups. As an interesting example we apply it obtaining a…