Studia Mathematica

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Operational Calculus

Pure and Applied Mathematics, Volume 109: Operational Calculus, Second Edition. Volume I presents the foundations of operational calculus and its applications to physics and engineering. This book introduces the operators algebraically as a kind of fractions. Organized into three parts, this volume begins with an overview of the concept as well as the characteristics of a convolution of continuous functions. This text then examines the transitivity, associativity, and distributivity of convolution with regard to addition. Other parts consider the methods of solving other difference equations, particularly in the field of electrical engineering, in which the variable runs over integer values only. This book discusses as well the solution of differential equations under given initial conditions. The final part deals with the characteristic properties of a derivative and provides the definition of algebraic derivative to any operators. This book is a valuable resource for physicists, electrical engineers, mathematicians, and research workers.
Fredholm Theory in Banach Spaces

Author: Anthony Francis Ruston
language: en
Publisher: Cambridge University Press
Release Date: 2004-06-03
Presents analogues for operators on Banach spaces of Fredholm's solution of integral equations of the second kind.
Mathematician for All Seasons

This book presents, in his own words, the life of Hugo Steinhaus (1887–1972), noted Polish mathematician of Jewish background, educator, and mathematical popularizer. A student of Hilbert, a pioneer of the foundations of probability and game theory, and a contributor to the development of functional analysis, he was one of those instrumental to the extraordinary flowering of Polish mathematics before and after World War I. In particular, it was he who “discovered” the great Stefan Banach. Exhibiting his great integrity and wit, Steinhaus’s personal story of the turbulent times he survived – including two world wars and life postwar under the Soviet heel – cannot but be of consuming interest. His account of the years spent evading Nazi terror is especially moving. The steadfast honesty and natural dignity he maintained while pursuing a life of demanding scientific and intellectual enquiry in the face of encroaching calamity and chaos show him to be truly a mathematician for all seasons. The present work will be of great interest not only to mathematicians wanting to learn some of the details of the mathematical blossoming that occurred in Poland in the first half of the 20th century, but also to anyone wishing to read a first-hand account of the history of those unquiet times in Europe – and indeed world-wide – by someone of uncommon intelligence and forthrightness situated near an eye of the storm.