Abstract: This collection of papers deals with investigations into various problems in the theory of differentiable functions of many variables and its applications to differential equations and numerical methods of their solution.
Embeddings of various spaces of differentiable functions are obtained and their dependence on domain of definition of functions is studied. Multiplicators are studied and basises in weighted spaces are constructed. Various approximations of smooth functions and their representations with the use of series and integrals are considered in details. Also studied are a number of spectral problems related to ordinary differential operators with singular coefficients, and solutions of regular partial differential equations with emphasis on their behaviour at infinity; block method for approximate solution of Laplace equation is developed.
Preceding parts of the present collection are published in the Proceedings of the Steklov Institute of Mathematics: pt. 1 – vol. 77 (1965), pt. 2 – vol. 89 (1967), pt. 3 – vol. 105 (1969), pt. 4 – vol. 117 (1972), pt. 5 – vol. 131 (1974), pt. 6 – vol. 140 (1976), pt. 7 – vol. 150 (1979), pt. 8 – vol. 156 (1980), pt. 9 – vol. 161 (1983), pt. 10 – vol. 170 (1985), pt. 11 – vol. 173 (1986), pt. 12 – vol. 181 (1988).
This book is aimed at scientists, students and postgraduate students specializing in the theory of functions and its applications.
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