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140122  eng 
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a 9789401146098

100 
1 

a Khrennikov, Andrei Y.

245 
0 
0 
a Superanalysis
h Elektronische Ressource
c by Andrei Y. Khrennikov

250 


a 1st ed. 1999

260 


a Dordrecht
b Springer Netherlands
c 1999, 1999

300 


a IX, 357 p
b online resource

505 
0 

a 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 

505 
0 

a 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

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a 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 

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a Mathematical analysis

653 


a Analysis

653 


a Mathematical physics

653 


a Analysis (Mathematics)

653 


a Theoretical, Mathematical and Computational Physics

710 
2 

a SpringerLink (Online service)

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0 
7 
a eng
2 ISO 6392

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b SBA
a Springer Book Archives 2004

490 
0 

a Mathematics and Its Applications

856 


u https://doi.org/10.1007/9789401146098?nosfx=y
x Verlag
3 Volltext

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0 

a 515

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a 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, during the next twenty years, the algebraic apparatus de veloped by Martin was used in all mathematical works. We must point out here the considerable contribution made by F. A. Berezin, G 1. Kac, D. A. Leites, B. Kostant. In their works, they constructed a new division of mathematics which can naturally be called an algebraic superanalysis. Following the example of physicists, researchers called the investigations carried out with the use of commuting and anticom muting coordinates supermathematics; all mathematical objects that appeared in supermathematics were called superobjects, although, of course, there is nothing "super" in supermathematics. However, despite the great achievements in algebraic superanaly sis, this formalism could not be regarded as a generalization to the case of commuting and anticommuting variables from the ordinary Newton analysis. What is more, Schwinger's formalism was still used in practically all physical works, on an intuitive level, and physicists regarded functions of anticommuting variables as "real functions" == maps of sets and not as elements of Grassmann algebras. In 1974, Salam and Strathdee proposed a very apt name for a set of super points. They called this set a superspace
