Harmonic functions - the solutions of Laplace's equation - play a crucial role in many areas of mathematics, physics, and engineering. Avoiding the disorganization and inconsistent notation of other expositions, the authors approach the field from a more function-theoretic perspective, emphasizing techniques and results that will seem natural to mathematicians comfortable with complex function theory and harmonic analysis; prerequisites for the book are a solid foundation in real and complex analysis together with some basic results from functional analysis. Topics covered include: basic properties of harmonic functions defined on subsets of Rn, including Poisson integrals; properties bounded functions and positive functions, including Liouville's and Cauchy's theorems; the Kelvin transform; Spherical harmonics; hp theory on the unit ball and on half-spaces; harmonic Bergman spaces; the decomposition theorem; Laurent expansions and classification of isolated singularities; and boundary behavior. An appendix describes routines for use with MATHEMATICA to manipulate some of the expressions that arise in the study of harmonic functions.

Harmonic Function Theory (Graduate Texts in Mathematics, Vol 137)

Science & Math

Axler, Sheldon

Bourdon, Paul

Ramey, Wade

Mathematics

Springer, Verlag

The accidental discovery of a decades old murder thrusts a young American diplomat in modern day Berlin into a terrifying race against time to destroy an underground menace that has lain dormant since the closing days of World War II. An obscure murder in the last days of World War II, a demonic plot that remains shrouded in time... Either through fate, accidental circumstance, or even the hand of God, a horror begins to surface and unfold. But is it too late to change its catastrophic outcome?

The Sentinel

Literature & Fiction

Genre Fiction

Paul Bourdon

In post communist Russia, there are no rules... For those in pursuit of wealth and power, there are no limits to what they'll do to obtain it. Even the unthinkable. Emerging technology has collided with Dark Age mentality in the vortex of a perfect storm. The paradigm has changed. At the highest levels, criminal minds have become emboldened to use the mask of terrorism to go where the sinister mind has never before dared.

Trojan Horse

The Aquitaine Deception

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Books by Bourdon, Paul