UID:
almahu_9947367865002882
Umfang:
1 online resource (389 p.)
ISBN:
1-281-79030-3
,
9786611790301
,
0-08-087195-X
Serie:
North-Holland mathematics studies ; 84
Inhalt:
This volume presents a new mathematical theory of generalized functions, more general than Distribution Theory, giving a rigorous mathematical sense to any product of a finite number of distributions and to heuristic computations of Quantum Field Theory. Although the physical motivations are emphasized, the book is also addressed to mathematicians with no knowledge of physics. This work opens a new domain of research in both pure and applied mathematics.
Anmerkung:
Description based upon print version of record.
,
Front Cover; New Generalized Functions and Multiplication of Distributions; Copyright Page; CONTENTS; PART I: INTRODUCTION TO THE MULTIPLICATION OF DISTRIBUTIONS; Chapter 1. A Review of the Classical Heuristic Computations of Quantum Field Theory; 1.1 - A brief historical survey; 1.2 - A Fock space; 1.3 - A free field; 1.4 - An interacting field equation; 1.5 - The canonical Hamiltonian formalism; 1.6 - Interacting field operators; 1.7 - The scattering operator; 1.8 - Wick products of free fields operators; Chapter 2. A Review of Some Products of Distributions
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2.1 - The method of regularization and passage to the limit2.2 - The Fourier transform method; 2.3 - Comparison of the two methods; 2.4 - Schwartz's impossibility result; Chapter 3. A General Multiplication of Distributions; 3.1 - Description of the basic idea; 3.2 - A concept of partial derivatives generalizing derivation in the distribution sense; 3.3 - A property of all c8 functions over E' (ohm); 3.4 - Construction of the algebra G(ohm); 3.5 - Connection with classical products; 3.6 - Non linear functions of elements of G(ohm); PART II: A GENERALIZED MATHEMATICAL ANALYSIS
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Chapter 4. Concepts of Generalized Functions4.1 - The use of germs of C8 functions on open sets of D(ohm); 4.2 - Another concept of generalized functions: The algebra Gs(ohm); 4.3 - Examples of solutions of differential equations; 4.4 - Some useful results; 4.5 - Local generalized functions; 4.6 - Restrictions of generalized functions to subspaces; 4.7 - Global weak solutions of ordinary differential equations; 4.8 - Examples of modifications of the concepts of generalized functions; 4.9 - Modifications of the sets Aq and ""Removal of divergences""
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Chapter 5. Pointvalues of Generalized Functions5.1 - Construction of the algebra C; 5.2 - Nonlinear properties of C; 5.3 - Point values of generalized functions; 5.4 - Examples; 5.5 - Constant generalized functions; 5.6 - Dependence of C on the space dimension; Chapter 6. Integration of Generalized Functions; 6.1 - The integral of a generalized function on a compact set; 6.2 - Connections with classical integrals; 6.3 - Primitives; 6.4 - Convolution; 6.5 - Fourier transform; Chapter 7. Generalized Functions as Boundary Values of Usual C8 Functions
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7.1 - A simplification in the concepts of generalized functions7.2 - Pointvalues; 7.3 - Integration; 7.4 - Convolution; 7.5 - Generalized functions considered as ""generalized distributions""; 7.6 - Fourier transform; 7.7 - Extension of domains and simplifications; 7.8 - Composition of generalized functions; Chapter 8. Holomotphic Generalized Functions; 8.1 - Integrals along curves; 8.2 - Definition and first examples of holomorphic generalized functions; 8.3 - Generalized Cauchy formulas
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8.4 - Characterization of holomorphic generalized functions as boundary values of usual holomorphic functions
,
English
Weitere Ausg.:
ISBN 0-444-86830-5
Sprache:
Englisch
