The Theory Of Linear Operators

Description: Please refer to the section BELOW (and NOT ABOVE) this line for the product details - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Title:The Theory Of Linear OperatorsISBN13:9781443731492ISBN10:1443731498Author:Davis, Harold T. (Author)Description:The Theory Of Linear Operators From The Standpoint Of Differen Tial Equations Of Infinite Order By Harold T Davis Originally Published In 1936 Contents Include: Chapter I Linear Operators 1 The Nature Of Operators ------------1 2 Definition Of An Operator ----- --3 3 A Classification Of Operational Methods --------7 4 The Formal Theory Of Operators ----------G 5 Generalized Integration And Differentiation - - 16 6 Differential And Integral Equations Of Infinite Order -----23 7 The Generatrix Calculus - - 28 8 The Heaviside Operational Calculus ---------34 9 The Theory Of Functionals ------------33 10 The Calculus Of Forms In Infinitely Many Variables -----4 Chapter Ii Particular Operators 1 Introduction ----------------51 2 Polynomial Operators --------53 3 The Fourier Definition Of An Operator ---------53 4 The Operational Symbol Of Von Neumann And Stone -----57 5 The Operator As A Laplace Transform ---------59 6 Polar Operators -60 7 Branch Point Operators ------------64 8 Note On The Complementary Function ---------70 9 Riemanns Theory - -- --72 10 Functions Permutable With Unity ----------76 11 Logarithmic Operators ------------78 12 Special Operators --------------85 13 The General Analytic Operator ----------99 14 The Differential Operator Of Infinite Order -------100 15 Differential Operators As A Cauchy Integral -------103 16 The Generatrix Of Differential Operators --------104 17 Five Operators Of Analysis ------------105 Chapter Iii The Theory Of Linear Systems Of Equations 1 Preliminary Remarks -------------108 2 Types Of Matrices --------------109 3 The Convergence Of An Infinite Determinant -------114 4 The Upper Bound Of A Determinant Hadamards Theorem - - 116 5 Determinants Which Do Not Vanish - - - - - - - - - 123 6 The Method Of The Liouville-Neumann Series -------126 7 The Method Of Segments ------------130 8 Applications Of The Method Of Segments --------132 9 The Hilbert Theory Of Linear Equations In An Infinite Number Of Variables - - - - 137 10 Extension Of The Foregoing Theory To Holder Space 149 Chapter Iv Operational Multiplication And Inversion 1 Algebra And Operators ------- --153 2 The Generalized Formula Of Leibnitz ---------154 3 Bourlets Operational Product -- 155 4 The Algebra Of Functions Of Composition --------159 5 Selected Problems In The Algebra Of Permutable Functions - - - - 164 G The Calculation Of A Function Permutable With A Given Function - 166 7 The Transformation Of Peres -----------171 8 The Permutability Of Functions Permutable With A Given Function - 173 9 Permutable Functions Of Second Kind - --176 10 The Inversion Of Operators Bourlets Theory ------177 It The Method Of Successive Substitutions --------181 12 Some Further Properties Of The Resolvent Generatrix - 185 13 The Inversion Of Operators By Infinite Differentiation - 188 14 The Permutability Of Linear Pilyeiential Operators -----190 15 A Class Of Non-Permutable Operators ---------194 16 Special Examples Illustrating The Application Of Operational Processes 200 Chapter V Grades Defined By Special Operators 1 Definition ----------------211 2 The Grade Of An Unlimitedly Differentiable Function - 212 3 Functions Of Finite Grade ------------215 4 Asymptotic Expansions --- 222 5 The Summability Of Differential Operators With Constant Coefficients 230 6 The Summability Of Operators Of Laplace Type ------235 Chapter Vi Differential Equations Of Infinite Order With Constant Coefficients 1 Introduction ---------------238 2 Expansion Of The Resolvent Generatrix --------239 3 The Method Of Cauchy-Bromwich ----------250 4 Binding:Hardcover, HardcoverPublisher:MYERS PRPublication Date:2008-11-04Weight:2.13 lbsDimensions:1.56'' H x 8.5'' L x 5.5'' WNumber of Pages:648Language:English

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Location: USA

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