Riemann's Boundary Problem with Infinite Index

Riemann's Boundary Problem with Infinite Index

Paperback(Softcover reprint of the original 1st ed. 1994)

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Product Details

ISBN-13: 9783034896559
Publisher: Birkh�user Basel
Publication date: 10/10/2012
Series: Operator Theory: Advances and Applications , #67
Edition description: Softcover reprint of the original 1st ed. 1994
Pages: 252
Product dimensions: 0.00(w) x 0.00(h) x 0.02(d)

Table of Contents

I.- General Properties of Analytic and Finite Order Functions in the Half-Plane.- 1 Definition of order and indicator of a function holomorphic in an angle. Relations between various definitions of order..- 2 Generalized Nevanlinna and Carleman formulas.- 3 Canonical representation of a function of finite order in the half-plane.- Necessary Conditions of Completely Regular Growth in the Half-Plane.- 4 Definition of completely regular growth in the half-plane. List of results on completely regular growth.- 5 Relation between completely regular growth in open and closed angles.- 6 Asymptotic behavior of the modulus and zero distributions of entire functions of the class A*?.- 7 Existence of argument boundary density for the zero set of a function from the class A*?.- 8 Existence of boundary and argument densities for the zero set of a function from A*?.- Sufficient Conditions of Completely Regular Growth in The Half-Plane and Formulas For Indicators.- 9 The growth of some auxiliary functions of non-integer order.- 10 A criterion for a function to belong to the class A*?, ? being non-integer.- 11 A criterion for a function to belong to the class ¯A*?, ? being non-integer.- 12 The argument-boundary symmetry of the zero set of a function of the class A*?, ? being integer.- 13 The growth of some auxiliary functions of integer order.- 14 A criterion for a function to belong to the class A*?, ? integer.- 15 A criterion for a function to belong to the class ¯A*?, ? integer.- 16 Functions of the class ¯A*? for even and for odd ?.- 17 Functions of a finite degree in the half-plane.- II.- Riemann Boundary Problem With an Infinite Index When the Verticity Index is Less Than 1/2.- 18 Statement of the homogeneous problem.- 19 Canonical function.- 20 Solution of the homogeneous problem in the class BL. Description of solutions of order ?.- 21 Formulation of the non-homogeneous problem and an approach to its solution.- 22 Solution of the non-homogeneous problem.- Riemann Boundary Problem With Infinite Index in The Case Of Verticity of Infinite Order.- 23 Statement of the homogeneous problem.- 24 Canonical function.- 25 Asymptotic properties of zero sets of solutions of the homogeneous problem from the classes B and B*?.- 26 General form of solutions of the homogeneous problem in the class B.- 27 General form of solutions of the homogeneous problem in the class B*?.- 28 An example of a solution of the homogeneous problem in the class B?. Importance of the restriction on the exponent in the Hölder condition for the function ?(t) = arg G(t)/(2?t?).- 29 Statement of the non-homogeneous problem and an approach to its solution.- 30 Auxiliary statements.- 31 Solution of the homogeneous problem.- Riemann Boundary Problem With A Negative Index.- 32 An example of a solvable homogeneous problem with a negative index.- 33 Conditions of unsolvability of the homogeneous problem with a negative index.- 34 Conditions of solvability of the non-homogeneous problem with an index — ?.- On the Paley Problem.- A.1 Formulation of the problem and proff of the main inequality.- A.2 Solution of the Paley problem.

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