Book

Real Induces Complex: Mathematical Analysis

October 2022

Authors:

Babayo Abdullahi

Federal University, Kashere

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Economic complexity: From useless to keystone

January 2018 · Nature Physics

Cesar Hidalgo

p>Technological innovation seems to be dominated by chance. But a new mathematical analysis suggests we might be able to anticipate when seemingly useless technologies become keystones of more complex environments.</p

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Moser-Trudinger and Beckner-Onofri's inequalities on the CR sphere

December 2007 · Annals of Mathematics

We derive sharp Moser-Trudinger inequalities on the CR sphere. The first type is in the Adams form, for powers of the sublaplacian and for general spectrally defined operators on the space of CR-pluriharmonic functions. We will then obtain the sharp Beckner-Onofri inequality for CR-pluriharmonic functions on the sphere, and, as a consequence, a sharp logarithmic ... [Show full abstract] Hardy-Littlewood-Sobolev inequality in the form given by Carlen and Loss.

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Recent Developments in Applied Pseudoanalytic Function Theory

November 2006

Vladislav V Kravchenko

We present recently obtained results in the theory of pseudoanalytic functions and its applications to elliptic second-order equations. The operator (divpgrad+q) with p and q being real valued functions is factorized with the aid of Vekua type operators of a special form and as a consequence the elliptic equation (divpgrad+q)u=0, (1) reduces to a homogeneous Vekua equation describing generalized ... [Show full abstract] analytic (or pseudoanalytic) functions. As a tool for solving the Vekua equation we use the theory of Taylor and Laurent series in formal powers for pseudoanalytic functions developed by L. Bers. The series possess many important properties of the usual analytic power series. Their applications until recently were limited mainly because of the impossibility of their explicit construction in a general situation. We obtain an algorithm which in a really broad range of practical applications allows us to construct the formal powers and hence the pseudoanalytic Taylor series in explicit form precisely for the Vekua equation related to equation (1). In other words, in a bounded domain this gives us a complete (in C-norm) system of exact solutions of (1).

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Last Updated: 09 Oct 2022