Charles N. Moore's Books

Probabilistic Behavior of Harmonic Functions

By: Rodrigo Banuelos,Charles N. Moore

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Probabilistic Behavior of Harmonic Functions

By: Rodrigo Banuelos,Charles N. Moore

Harmonic analysis and probability have long enjoyed a mutually beneficial relationship that has been rich and fruitful. This monograph, aimed at researchers and students in these fields, explores several aspects of this relationship. The primary focus of the text is the nontangential maximal function and the area function of a harmonic function and their probabilistic analogues in martingale theory. The text first gives the requisite background material from harmonic analysis and discusses known results concerning the nontangential maximal function and area function, as well as the central and essential role these have played in the development of the field.The book next discusses further refinements of traditional results: among these are sharp good-lambda inequalities and laws of the iterated logarithm involving nontangential maximal functions and area functions. Many applications of these results are given. Throughout, the constant interplay between probability and harmonic analysis is emphasized and explained. The text contains some new and many recent results combined in a coherent presentation.

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Page Count

220

Publisher

Birkhäuser

Published Date

ISBN 10

3034887280

ISBN 13

9783034887281

The History of Pioneer Lexington, 1779-1806

By: Charles R. Staples

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The History of Pioneer Lexington, 1779-1806

By: Charles R. Staples

In this study of Kentucky pioneer life, Charles R. Staples creates a colorful record of Lexington's first twenty-seven years. He writes of the establishment of an urban center in the midst of the frontier expansion, and in the process documents Lexington's vanishing history. Staples begins with the settlement of the town, describing its early struggles and movement toward becoming the "capitol" of Fayette County. He also presents interesting pictures of the early pioneers and their livelihood: food, dress, houses, cooking utensils, "house raisings," religious meetings, horse races, and other types of entertainment. First published in 1939, this reprint provides those interested in the early history of Kentucky with a comprehensive look at Lexington's pioneer period. Staples recreates a time when downtown's busiest streets were still wilderness and a land rich with agricultural potential was developing commercial elements. Because he wrote during a period when much of pioneer Lexington remained, he provides a wealth of primary information that could not be assembled again.

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