Infinite Electrical Networks

Armen H. Zemanian (Autor)

Buch | Hardcover

324 Seiten

1991
Cambridge University Press (Verlag)
978-0-521-40153-1 (ISBN)

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This book presents the salient features of the general theory of infinite electrical networks in a coherent exposition. Using the basic tools of functional analysis and graph theory, the author examines the fundamental developments in the field and discusses applications to other areas of mathematics. The first half of the book presents existence and uniqueness theorems for both infinite-power and finite-power voltage-current regimes, and the second half discusses methods for solving problems in infinite cascades and grids. A notable feature is the invention of transfinite networks, roughly analogous to Cantor's extension of the natural numbers to the transfinite ordinals. The last chapter is a survey of application to exterior problems of partial differential equations, random walks on infinite graphs, and networks of operators on Hilbert spaces.

1. Introduction; 2. Infinite-power regimes; 3. Finite-power regimes: the linear case; 4. Finite-power regimes: the nonlinear case; 5. Transfinite electrical networks; 6. Cascades; 7. Grids; 8. Applications.

Erscheint lt. Verlag	29.11.1991
Reihe/Serie	Cambridge Tracts in Mathematics
Zusatzinfo	93 Line drawings, unspecified
Verlagsort	Cambridge
Sprache	englisch
Maße	158 x 238 mm
Gewicht	600 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Graphentheorie
ISBN-10	0-521-40153-4 / 0521401534
ISBN-13	978-0-521-40153-1 / 9780521401531
Zustand	Neuware