Encyclopaedia of Mathematics: Stochastic Approximation — Zygmund Class of Functions
Springer Science & Business Media, Jan 31, 1993 - Mathematics - 536 pages
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
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1980 Subject Classification Acad algorithm Amer AMS 1980 Subject analysis analytic arbitrary boundary bounded calculus called coefficients commutative compact complex convergence coordinates corresponding curve defined denoted differential equations dimensional distribution domain dynamics Editorial comments elements equivalent example exists field finite formula func function functor geometry given group G homomorphism imbedding infinite integral invariant isomorphic lattice Lie algebra Lie groups linear locally convex space manifold mapping Math mathematical matrix metric module morphism obtained operator plane polynomials problem properties References A1 representation respect ring Russian satisfies semi-groups sequence solution Springer stochastic process structure subgroup subharmonic functions subset subspace summation method surface symmetric tangent tensor theorem theory tion topological group topological space topological vector space transformation translated trigonometric uniform unique Univ universal algebras values variational variety vector bundle vector space von Neumann algebra Weierstrass zero