Encyclopaedia of Mathematics, Volume 5
Springer Science & Business Media, Dec 1, 2013 - Mathematics - 534 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 fine 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 Abelian Acad Akad algebraic groups algebraic variety Amer AMS 1980 Subject analytic analytic function approximation arbitrary boundary calculus called coefficients cohomology compact complex convergence corresponding curve defined differential equations dimensional distribution domain Editorial comments eigen values elements equivalent example exists field finite finite-dimensional formula func function f geometry given group G homomorphism ideal imbedding improper integral inequality infinite integral equations interpolation invariant inverse irreducible isometric isomorphic Jacobi kernel knot Krein space Lagrange Laplace lattice Lebesgue Lie algebra Lie groups linear algebraic groups linear operator manifold mapping Math mathematical matrix measure method metric morphism Nauk nilpotent obtained polynomials problem properties random variables References A1 representation respect Riemannian ring Russian semi-group semi-simple sequence solution solvable Springer subalgebra subgroup subspace surface theorem theory tion topological topological space transformations translated Univ vector space zero