Description: 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.
Description: These lecture notes are an introduction to undergraduate real analysis. They cover the real numbers and one-variable calculus.
Description: This note covers the following topics: Finite Fourier Transform, Sunspots, Periodic Time Series, ftmatrix, Other Fourier Transforms and Series.
Description: This book covers the following topics: Fourier transform on L1, Tempered distribution, Fourier transform on L2, Interpolation of operators, Hardy-Littlewood maximal function, Singular integrals, Littlewood-Paley theory, Fractional integration, Singular multipliers, Bessel functions, Restriction to the sphere and Uniform sobolev inequality.
Description: This note covers the following topics: Sets, The Real Numbers, Sequences, Series, Functions, Power Series and The elementary fun.
Description: 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.
Description: This note covers the following topics: Vector Spaces with Inner Product, Fourier Series, Fourier Transform, Windowed Fourier Transform, Continuous wavelets, Discrete wavelets and the multiresolution structure, Continuous scaling functions with compact support.
Description: This note covers the following topics: Introduction and terminology, Fourier series, Convergence of Fourier series, Integration of Fourier series, Weierstrass approximation theorem, Applications to number theory, The isoperimetric inequality and Ergodic theory.
Description: This note explains the following topics: Banach Spaces, Gelfand Theory and C* algebras, The Spectral Theorem, Positive elements of a C* algebra and Homomorphisms.
Description: This note covers the following topics: Hahn-Banach Theorems and Introduction to Convex Conjugation, Baire Category Theorem and Its Application, Weak Topology, Bounded (Linear) Operators and Spectral Theory, Compact and Fredholm Operators.
Description: This note explains the following topics: Banach Spaces, Linear Operators, Baire Category Theorem, The Hahn-Banach Theorem, Hamel Bases, Projections, The Dual Space, Topological Spaces, Product Spaces.
Description: This note provides the details about the following topics: Nonlinear equations, Linear Systems, Eigenvalues, Nonlinear systems, Ordinary Differential Equations, Fourier transforms.
Description: This note covers the following topics: Baire category, Non-existence of functions of several variables, The principle of uniform boundedness, Zorn's lemma and Tychonov's theorem, The Hahn-Banach theorem, Banach algebras, Maximal ideals, Analytic functions, The Gelfand representation.
Description: Thesis (PH. D.)--University of Chicago, 1916
Description: English, French, German
Geometry, Descriptive