Algebraic Structures and Operator Calculus
Springer (Verlag)
978-94-010-4720-3 (ISBN)
I. General remarks.- II. Some notations.- III. Gamma and beta functions.- IV. Numbering.- V. References.- VI. Polynomials: notations and formulas.- VII. Exercises and examples.- 1 Introductory Noncommutative Algebra.- I. Representations.- II. Heisenberg-Weyl algebra.- III. sl(2) algebra.- IV. Splitting formulas.- V. Exercises and examples.- 2 Hypergeometric functions.- I. Notations.- II. Generating function for 2F1.- III. General formulation of CVPS and transformation formulas.- IV. Formulas related to HW algebra.- V. Formulas related to sl(2) algebra.- VI. Exercises and examples.- 3 Probability and Fock Spaces.- I. Trace functionals: probability and operators.- II. Fock spaces.- III. Tensor products.- IV. Exercises and examples.- 4 Moment Systems.- I. Moment generating functions and convolution.- II. Moment systems.- III. Radial moment systems.- IV. Holomorphic canonical variables.- V. Exercises and examples.- 5 Bernoulli Processes.- I. Bernoulli systems: general structure.- II. Binomial process and Krawtchouk polynomials.- III. Negative binomial process and Meixner polynomials.- IV. Continuous binomial process and Meixner-Pollaczek polynomials.- V. Poisson process and Poisson-Charlier polynomials.- VI. Exponential process and Laguerre polynomials.- VII. Brownian motion and Hermite polynomials.- VIII. Canonical moments.- IX. Exercises and examples.- 6 Bernoulli Systems.- I. Expansions, Rodrigues, and Riccati.- II. w-kernel.- III. X operator.- IV. Generating functions.- V. Riccati equations and Bernoulli systems.- VI. Reproducing kernels.- VII. Exercises.- 7 Matrix Elements.- I. Matrix elements.- II. Addition formulas and Riccati equations.- III. Coherent states and coherent state representations.- IV. Addition formulas for matrix elements of the group.- V. Exercises.-References.
Reihe/Serie | Mathematics and Its Applications ; 241 | Mathematics and Its Applications ; 241 |
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Zusatzinfo | IX, 226 p. |
Verlagsort | Dordrecht |
Sprache | englisch |
Maße | 160 x 240 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Analysis | |
ISBN-10 | 94-010-4720-0 / 9401047200 |
ISBN-13 | 978-94-010-4720-3 / 9789401047203 |
Zustand | Neuware |
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