Author | Polishchuk, Efim M. author |
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Title | Continual Means and Boundary Value Problems in Function Spaces [electronic resource] / by Efim M. Polishchuk |
Imprint | Basel : Birkhรคuser Basel, 1988 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-9171-4 |
Descript | 160 p. online resource |
1. Functional Classes and Function Domains. Mean Values. Harmonicity and the Laplace Operator in Function Spaces -- 1. Functional classes -- 2. Function domains -- 3. Continual means -- 4. The functional Laplace operator -- 2 Chapter 2. The Laplace and Poisson Equations For a Normal Domain -- 5. Boundary value problems for a normal domain with boundary values on the Gรขteaux ring -- 6. Semigroups of continual means. Relations to the probability solutions of classical boundary value problems. Applications of the integral over a regular measure -- 3. The Functional Laplace Operator and Classical Diffusion Equations. Boundary Value Problems for Uniform Domains. Harmonic Controlled Systems -- 7. Boundary value problems with strong Laplacian and their parallelism to classical parabolic equations -- 8. Boundary value problems for uniform domains -- 9. Harmonic control systems -- 4. General Elliptic Functional Operators on Functional Rings -- 10. The Dirichlet problem in the space of summable functions and related topics -- 11. The generalized functional Poisson equation -- Comments -- References