Analysis IV - Linear and Boundary Integral Equations

Maz'Ya, V. G.

ISBN 10: 0387519971 / ISBN 13: 9780387519975

Published by Springer Verlag, 1991

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Bibliographic Details

• Title: Analysis IV - Linear and Boundary Integral Equations
• Publisher: Springer Verlag
• Publication Date: 1991
• Language: English
• ISBN 10: 0387519971
• ISBN 13: 9780387519975
• Binding: Hardcover
• Condition: New

About this title

Synopsis

A linear integral equation is an equation of the form XEX. (1) 2a(x)cp(x) - Ix k(x, y)cp(y)dv(y) = f(x), Here (X, v) is a measure space with a-finite measure v, 2 is a complex parameter, and a, k, f are given (complex-valued) functions, which are referred to as the coefficient, the kernel, and the free term (or the right-hand side) of equation (1), respectively. The problem consists in determining the parameter 2 and the unknown function cp such that equation (1) is satisfied for almost all x E X (or even for all x E X if, for instance, the integral is understood in the sense of Riemann). In the case f = 0, the equation (1) is called homogeneous, otherwise it is called inhomogeneous. If a and k are matrix functions and, accordingly, cp and f are vector-valued functions, then (1) is referred to as a system of integral equations. Integral equations of the form (1) arise in connection with many boundary value and eigenvalue problems of mathematical physics. Three types of linear integral equations are If 2 = 0, then (1) is called an equation of the first kind; if 2a(x) i= 0 for all x E X, then (1) is termed an equation of the second kind; and finally, if a vanishes on some subset of X but 2 i= 0, then (1) is said to be of the third kind.

From the Back Cover

This book is a companion to Byrnes's award-winning Lunar Orbiter Photographic Atlas of the Near Side of the Moon (Springer, 2005). It provides comprehensive coverage of the far side of the Moon, and is the first book that collects photographs from all five Lunar Orbiter missions: Clementine, Apollo, Luna, Zond, and Nozomi. As in the previous book, the scanning artifacts of the Lunar Orbiter photos have been cleaned.
The photographs show each part of the far side in the most favorable resolution and sun angle. There are many high-altitude oblique photos that provide a feeling of being in space; this book is more like a photographic tour of the far side than an atlas.  The striking differences between the near and far side have been a major mystery for astronomers but this book suggests an explanation: a massive early impact on the near side produced the Near Side Megabasin; an impact so large that its rim is on the far side. The floor of this basin established the canvas for the portrait of the Man in the Moon and its ejecta prepared the far side for the rugged array of basins and craters shown in these photos.
Since many professional and amateur astronomers direct their telescopes to the near side of the Moon; these photos provide a unique opportunity to become familiar with the far side!