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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 
Lecture Notes Classical Fourier Analysis
This note explains the following topics: Fourier Transform, Fourier Inversion and Plancherel’s Theorem, The Little wood Principle and Lorentz Spaces, Relationships Between Lorentz Quasinorms and Lp Norms, Banach Space Properties of Lorentz Spaces, Hunt’s Interpolation Theorem, Proofs of Interpolation Theorems, Interpolation and Kernels, Boundedness of Calderon Zygmund Convolution Kernels, Lp Bounds for Calderon Zygmund Convolution Kernels, The Mikhlin Multiplier Theorem, The Mikhlin Multiplier Theorem and Properties of Littlewood Paley Projections, Littlewood Paley Projections and Khinchines Inequality, The Fractional Chain Rule, Introduction to Oscillatory Integrals, Estimating Oscillatory Integrals With Stationary Phase, Oscillatory Integrals in Higher Dimensions.
Author(s): Monica Visan
105 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
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
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