CTM 166 The Lévy Laplacian (Cambridge Tracts in Mathematics) (M. N. Feller) 0521846226.pdf

CAMBRIDGE TRACTS IN MATHEMATICS
General Editors
b. bollobas, w. fulton, a. katok, f. kirwan,
p. sarnak, b. simon, b. totaro
166 The L´evy Laplacian
The L´evy Laplacian is an infinite-dimensional generalization of the well-known
classical Laplacian. Its theory has been increasingly well-developed in recent years
and this book is the first systematic treatment of it.
The book describes the infinite-dimensional analogues of finite-dimensional results,
and more especially those features that appear only in the generalized context. It
develops a theory of operators generated by the L´evy Laplacian and the symmetrized
L´evy Laplacian, as well as a theory of linear and nonlinear equations involving it.
There are many problems leading to equations with L´evy Laplacians and to
L´evy–Laplace operators, for example superconductivity theory, the theory of control
systems, the Gauss random field theory, and the Yang–Mills equation.
The book plemented by exhaustive bibliographic notes and references. The
result is a work that will be valued by those working in functional analysis, partial
differential equations and probability theory.
Cambridge Tracts in Mathematics
All the titles listed below can be obtained from good booksellers or from
Cambridge University Press. For plete series listing visit
http://publishing./stm/mathematics/ctm/
142. Harmonic Maps between Rienmannian Polyhedra. By J. Eells and
B. Fuglede
143. Analysis on Fractals. By J. Kigami
144. Torsors and Rational Points. By A. Skorobogatov
145. Isoperimetric Inequalities. By I. Chavel
146. Restricted Orbit Equivalence for Actions of Discrete Amenable Groups.
By J. W. Kammeyer and D. J. Rudolph
147. Floer Homology Groups in Yang–Mills Theory. By S. K. Donaldson
148. Graph Directed Markov Systems. By D. Mauldin and M. Urbanski
149. Cohomology of Vector Bundles and Syzygies. By J. Weyman
150. Harmonic Maps, Conservation Laws and Moving Frames. By F. Helein´
151. Frobenius Manifolds an