Table of Contents: Preface
1. Boundary Properties of Derivatives of the Poisson Integral for a
Half-Plane, pp. 1-19
1.1 Notation, Definitions and the Well-Known Statements
1.2 Auxiliary Statements
1.3 The Boundary Properties of Derivatives of the Poisson Integral for a Half-Plane
1.4 The Dirichlet Problem for a Half-Plane
2. Boundary Properties of Derivatives of the Poisson Integral for a
Circle, pp. 21-35
2.1 Notation and Definitions
2.2 Auxiliary Statements
2.3 Boundary Properties of Derivatives of the Poisson Integral for a Circle
2.4 The Dirichlet Problem for a Circle
3. Boundary Properties of Derivatives of the Poisson Integral for a
Ball, pp. 37-85
3.1 Notation, Definitions and Statement of Some Well-Known Facts
3.2 The Poisson Integral for a Ball
3.3 A Generalized Laplace Operator on the Unit Sphere Sk 1
3.4 Boundary Properties of the Integral DkU
3.5 The Boundary Properties of the Integral Drk
3.6 The Dirichlet Problem for a Ball
3.7 Representation by the Laplace Series of an Arbitrary Measurable
Function Defined on the Unit Sphere S2
4 Boundary Properties of Derivatives of the Poisson Integral for a
Space Rk+1 + (k > 1), 87-143
4.1 Generalized Partial First Order Derivatives of a Function of Several Variables
4.2 The Boundary Properties of First Order Partial Derivatives of the
Poisson Integral for a Half-Space Rk+1 + (k > 1)
4.3 Generalized Partial Second Order Derivatives for a Function of Several Variables
4.4 The Boundary Properties of Partial Second Order Derivatives of the Poisson Integral for a Half-Space Rk+1 + (k > 1)
4.5 The Dirichlet Problem for a Half-Space R3+
4.6 Generalized Partial Derivatives of Arbitrary Order
4.7 The Boundary Properties of Arbitrary Order Partial Derivatives of
the Poisson Integral for a Half-Space Rk+1
4.8 Generalized Mixed Derivatives and Differentials of Arbitrary Order
4.9 The Boundary Properties of Mixed Derivatives and Differentials of
Arbitrary Order of The Poisson Integral for the Half-Space Rk+1
+ (k > 1)
4.10 The Generalized Laplace Operator in Rk (k , 2)
4.11 The Boundary Properties of the Integral ¢rU(f; x; xk+1)
5. Boundary Properties of a Differentiated Poisson Integral for a cylinder,and Representation of a Function of Two Variables by a
Double Trigonometric Series, pp. 145-167
5.1 Notation and Definitions
5.2 Integral for a Bicylinder
5.3 Representation of a Function of Two Variables by a Trigonometric
Series in the Case of Spherical Convergence
5.4 On One Method of Summation of Double Fourier Series
5.5 Representation of a Function of Two Variables by a Double Trigonometric Series in the Case of Ptingsheim’s Convergence
Bibliography, pp. 169-177
Index |