Description: I Foundations of Infinite Dimensional Analysis.- 1. Linear operators on Hilbert spaces.- 2. Fock spaces and second quantization.- 3. Countably normed spaces and nuclear spaces.- 4. Borel measures on topological linear spaces.- II Malliavin Calculus.- 1. Gaussian probability spaces and Wiener chaos decomposition.- 2. Differential calculus of functionals, gradient and divergence operators.- 3. Meyer's inequalities and some consequences.- 4. Densities of non-degenerate functionals.- III Stochastic Calculus of Variation for Wiener Functionals.- 1. Differential calculus of It functionals and regularity of heat kernels.- 2. Potential theory over Wiener spaces and quasi-sure analysis.- 3. Anticipating stochastic calculus.- IV General Theory of White Noise Analysis.- 1. General framework for white noise analysis.- 2. Characterization of functional spaces.- 3. Products and Wick products of functionals.- 4. Moment characterization of distributions and positive distributions.- V Linear Operators on Distribution Spaces.- 1. Analytic calculus for distributions.- 2. Continuous linear operators on distribution spaces.- 3. Integral kernel operators and integral kernel representation for operators.- 4. Applications to quantum physics.- Appendix A Hermite polynomials and Hermite functions.- Appendix B Locally convex spaces amd their dual spaces.- 1. Semi-norms, norms and H-norms.- 2. Locally convex topological linear spaces, bounded sets.- 3. Projective topologies and projective limits.- 4. Inductive topologies and inductive limits.- 5. Dual spaces and weak topologies.- 6. Compatibility and Mackey topology.- 7. Strong topologies and reflexivity.- 8. Dual maps.- 9. Uniformly convex spaces and Banach-Saks' theorem.- Comments.- References.- Index of Symbols.

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