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Foundations of modern potential theory

Author: N S Landkof
Publisher: Berlin, New York, Springer-Verlag, 1972.
Series: Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Bd. 180.
Edition/Format:   Print book : EnglishView all editions and formats
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Additional Physical Format: Online version:
Landkof, N.S. (Naum Samoĭlovich).
Foundations of modern potential theory.
Berlin, New York, Springer-Verlag, 1972
(OCoLC)707452397
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: N S Landkof
ISBN: 0387053948 9780387053943 3540053948 9783540053941 9783642651854 3642651852
OCLC Number: 579100
Language Note: Translation of Osnovy sovremennoĭ teorii potentsiala.
Notes: Translation of Osnovy sovremennoĭ teorii potent︠s︡iala.
Description: x, 424 pages 24 cm.
Contents: 1. Spaces of measures and signed measures. Operations on measures and signed measures (No. 1-5).- 2. Space of distributions. Operations on distributions (No. 6-10)..- 3. The Fourier transform of distributions (No. 11-13).- I. Potentials and their basic properties.- 1. M. Riesz kernels (No. 1-3).- 2. Superharmonic functions (No. 4-5).- 3. Definition of potentials and their simplest properties (No. 6-9)...- 4. Energy. Potentials with finite energy (No. 10-15).- 5. Representation of superharmonic functions by potentials (No. 16-18).- 6. Superharmonic functions of fractional order (No. 19-25).- II. Capacity and equilibrium measure.- 1. Equilibrium measure and capacity of a compact set (No. 1-5).- 2. Inner and outer capacities and equilibrium measures. Capacitability (No. 6-10).- 3. Metric properties of capacity (No. 11-14).- 4. Logarithmic capacity (No. 15-18).- III. Sets of capacity zero. Sequences and bounds for potentials.- 1. Polar sets (No. 1-2).- 2. Continuity properties of potentials (No. 3-4).- 3. Sequences of potentials of measures (No. 5-8).- 4. Metric criteria for sets of capacity zero and bounds for potentials (No. 9-11).- IV. Balayage, Green functions, and the Dirichlet problem.- 1. Classical balayage out of a region (No. 1-6).- 2. Balayage for arbitrary compact sets (No. 7-11).- 3. The generalized Dirichlet problem (No. 12-14).- 4. The operator approach to the Dirichlet problem and the balayage problem (No. 15-18).- 5. Balayage for M. Riesz kernels (No. 19-23)...- 6. Balayage onto Borel sets (No. 24-25).- V. Irregular points.- 1. Irregular points of Borel sets. Criteria for irregularity (No. 1-6)...- 2. The characteristics and types of irregular points (No. 7-8)...- 3. The fine topology (No. 9-11).- 4. Properties of set of irregular points (No. 12-15).- 5. Stability of the Dirichlet problem. Approximation of continuous functions by harmonic functions (No. 16-22).- VI. Generalizations.- 1. Distributions with finite energy and their potentials (No. 1-5)...- 2. Kernels of more general type (No. 6-11).- 3. Dirichlet spaces (No. 12-15).- Comments and bibliographic references.
Series Title: Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Bd. 180.
Other Titles: Osnovy sovremennoĭ teorii potent︠s︡iala.
Responsibility: [by] N.S. Landkof. Translated from the Russian by A.P. Doohovskoy.
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