The main goal of this book is to present results pertaining to various versions of the maximum principle for elliptic and parabolic systems of arbitrary order. In particular, the authors present necessary and sufficient conditions for validity of the classical maximum modulus principles for systems of second order and obtain sharp constants in inequalities of Miranda-Agmon type and in many other inequalities of a similar nature. Somewhat related to this topic are explicit formulas for the norms and the essential norms of boundary integral operators. The proofs are based on a unified approach using, on one hand, representations of the norms of matrix-valued integral operators whose target spaces are linear and finite dimensional, and, on the other hand, on solving certain finite dimensional optimization problems. This book reflects results obtained by the authors, and can be useful to research mathematicians and graduate students interested in partial differential equations.
This volume contains a coherent point of view on various sharp pointwise inequalities for analytic functions in a disk in terms of the real part of the function on the boundary circle or in the disk itself. Inequalities of this type are frequently used in the theory of entire functions and in the analytic number theory.
A personal and philosophical meditation on the Hebrew Bible, its stories, and its sages. In this volume, Gershon Rubin attempts to draw the secrets of the antediluvian world into the modern day. Through the lens of a lifetime of spiritual learning, he explores the ancient saga of creation, Adam and Eve, and the generations to come after. As Rubin states by way of introduction to The Hebrew Saga, “My first name, Gershon, is similar to the Greek word geron (old man). Thus through my ‘geronoscope,’ I view the over-four-thousand-year-long written history of the Hebrew nation, which resulted in the origination of this my world-view, or world outlook.”
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