Superanalysis
defined as elements of Grassmann algebra (an algebra with anticom muting generators). The derivatives of these elements with respect to anticommuting generators were defined according to algebraic laws, and nothing like Newton's analysis arose when Martin's approach was used. Later, durin...
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Format:  eBook 
Language:  English 
Published: 
Dordrecht
Springer Netherlands
1999, 1999

Edition:  1st ed. 1999 
Series:  Mathematics and Its Applications

Subjects:  
Online Access:  
Collection:  Springer Book Archives 2004  Collection details see MPG.ReNa 
Table of Contents:
 I Analysis on a Superspace over Banach Superalgebras
 1. Differential Calculus
 2. CauchyRiemann Conditions and the Condition of ALinearity of Derivatives
 3. Integral Calculus
 4. Integration of Differential Forms of Commuting Variables
 5. Review of the Development of Superanalysis
 6. Unsolved Problems and Possible Generalizations
 II Generalized Functions on a Superspace
 1. Locally Convex Superalgebras and Supermodules
 2. Analytic Generalized Functions on the VladimirovVolovich Superspace
 3. Fourier Transformation of Superanalytic Generalized Functions
 4. Superanalog of the Theory of Schwartz Distributions
 5. Theorem of Existence of a Fundamental Solution
 6. Unsolved Problems and Possible Generalizations
 III Distribution Theory on an InfiniteDimensional Superspace
 1. Polylinear Algebra over Commutative Supermodules
 2. Banach Supermodules
 3. Hilbert Supermodules
 4. Duality of Topological Supermodules
 6. Cauchy Problem for Partial Differential Equations with Variable Coefficients
 7. NonArchimedean Supersymmetrical Quantum Mechanics
 8. Trotter Formula for nonArchimedean Banach Algebras
 9. Volkenborn Distribution on a nonArchimedean Superspace
 10. InfiniteDimensional nonArchimedean Superanalysis
 11. Unsolved Problems and Possible Generalizations
 VII Noncommutative Analysis
 1. Differential Calculus on a Superspace over a Noncommutative Banach Algebra
 2. Differential Calculus on Noncommutative Banach Algebras and Modules
 3. Generalized Functions of Noncommuting Variables
 VIII Applications in Physics
 1. Quantization in Hilbert Supermodules
 2. Transition Amplitudes and Distributions on the Space of Schwinger Sources
 References
 5. Differential Calculus on a Superspace over Topological Supermodules
 6. Analytic Distributions on a Superspace over Topological Supermodules
 7. Gaussian and Feynman Distributions
 8. Unsolved Problems and Possible Generalizations
 IV Pseudodifferential Operators in Superanalysis
 1. Pseudodifferential Operators Calculus
 2. The Correspondence Principle
 3. The FeynmanKac Formula for the Symbol of the Evolution Operator
 4. Unsolved Problems and Possible Generalizations
 V Fundamentals of the Probability Theory on a Superspace
 1. Limit Theorems on a Superspace
 2. Random Processes on a Superspace
 3. Axiomatics of the Probability Theory over Superalgebras
 4. Unsolved Problems and Possible Generalizations
 VI NonArchimedean Superanalysis
 1. Differentiale and Analytic Functions
 2. Generalized Functions
 3. Laplace Transformation
 4. Gaussian Distributions
 5. Duhamel nonArchimedean Integral. Chronological Exponent