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Classical Analysis and ODEs
This note explains the following topics: linearly related sequences of difference derivatives of discrete orthogonal polynomials, identity for zeros of Bessel functions, Close-to-convexity of some special functions and their derivatives, Monotonicity properties of some Dini functions, Classification of Systems of Linear Second-Order Ordinary Differential Equations, functions of Hausdorff moment sequences, Van der Corput inequalities for Bessel functions.
Author(s): arXiv.org
NA Pages 
Introduction to semi classical analysis for the Schrodinger operators
This note covers the following topics:From classical mechanics to quantum mechanics, Localized version Karadzhov, Uncertainty principle and Weyl term, Localization of the eigen functions, Short introduction to the h pseudo differential calculus, About global classes, Elliptic theory, Essential self adjointness and semi boundedness and functional calculus.
Author(s): B.Helffer
56 Pages
Lectures On Semiclassical Analysis
This note explains the following topics: Symplectic geometry, Fourier transform, stationary phase, Quantization of symbols, Semiclassical defect measures, Eigenvalues and eigenfunctions, Exponential estimates for eigenfunctions, symbol calculus, Quantum ergodicity and Quantizing symplectic transformations.
Author(s): Lawrence C. Evans and Maciej Zworski
211 Pages
First seven chapters of this monograph discuss the techniques involved in symbolic calculus have their origins in symplectic geometry. Remaining chapters explains wave and heat trace formulas for globally defined semi classical differential operators on manifolds and equivariant versions of these results involving Lie group actions.
Author(s): Victor Guillemin and Shlomo Sternberg
488 Pages
This note is for students to have mastered the knowledge of complex function theory in which the classical analysis is based. The main theme of this course note is to explain some fundamentals of classical transcendental functions which are used extensively in number theory, physics,engineering and other pure and applied areas.
Author(s): Edmund Y. M. Chiang
119 Pages