The Logarithmic potential and other monographs
著者
書誌事項
The Logarithmic potential and other monographs
Chelsea Pub. Co., 1980
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Monographs
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注記
Title on spine: Monographs
Includes bibliographical references
収録内容
- Evans, G. C. THe logarithmic potential
- Bliss, G. A. Fundamental existence theorems
- Kasner, E. Differential-geometric aspects of dynamics
内容説明・目次
内容説明
Contains the following monographs - ""The Logarithmic Potential"" by Evans, ""Fundamental Existence Theorems"" by Bliss, and ""Differential-Geometric Aspects of Dynamics"" by Kasner.
目次
- Preliminary Concepts. Stieltjes Integrals and Fourier Series: 1 Functions of limited variation
- 2 Continuation of the preceding
- 3 Integrals with respect to a function of limited variation
- 4 Note on the second law of the mean
- 5 Classical theorems on integrals and limits of integrals
- 6 The limits of Stieltjes integrals
- 7 Note on Lebesgue integrals
- 8 Convergence of Fourier series
- 9 Summability of series Functions Harmonic Within a Circle: 10 Preliminary theorems
- 11 A preliminary result
- 12 Note on integral identities
- 13 Digression: Functions of points and of point sets
- 14 Properties of the Poisson-Stieltjes integral
- 15 Continuation of the preceding: Behaviour of $u(r, \theta)$ in the neighborhood of the boundary
- 16 The Poisson integral: $F(\varphi)$ absolutely continuous Necessary and Sufficient Conditions. The Dirichlet Problems for the Circle: 17 Fundamental theorem and lemma
- 18 Proof of fundamental theorem
- 19 Special cases of the Poisson integral
- 20 The Dirichlet problem and its extension Potentials of a Single Layer and the Neumann Problem: 21 The Stieltjes integral for potentials of a single layer
- 22 Necessary and sufficient conditions
- 23 Further properties
- 24 The Neumann problems
- 25 General points of view
- 26 Digression: Physical interpretation of a general distribution of mass
- 27 Cauchy's integral formula General Simply Connected Plane Regions and the Order of Their Boundary Points: 28 Conformal transformations and general regions
- 29 Invariant forms of conditions (i), (ii) etc.
- 30 Invariant forms of conclusions
- 31 Order of boundary points
- 32 Integrals on the boundary and the Dirichlet problems
- 33 Special cases of the condition (ii). The continuous boundary value problem
- 34 A new continuous boundary value problem
- 35 The generalized Neumann problem in the general region Plane Regions of Finite Connectivity: 36 Functions harmonic outside a circle
- 37 The multiply connected region bounded by $n+1$ distinct circles
- 38 Representation in terms of the Green's function
- 39 Boundary integrals and Stieltjes integral equations
- 40 General regions of finite connectivity. Isolated point boundaries
- 41 Annular regions. Determination of the functions $F_0(\theta)$ and $F_1(\theta)$
- 42 Uniqueness of the representation of Theorem 3 for $S$ Related Problems: 43 A simple discontinuous boundary value problem
- 44 Continuous boundary value problems
- 45 Regions with continuous boundaries
- 46 Regions with rectifiable boundaries
- 47 Regions of infinite connectivity
- 48 Remarks on necessary and sufficient conditions
- 49 Convergence in the mean of positive order less than one
- 50 Integro-differential equations of Bocher type.
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