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The Theory Of Linear Operators by Harold T Davis, Hardcover | Indigo Chapters
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The Theory Of Linear Operators by Harold T Davis, Hardcover | Indigo Chapters
From Harold T Davis
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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... | The Theory Of Linear Operators by Harold T Davis, Hardcover | Indigo Chapters