Fourier series, Fourier transform and their applications to mathematical physics. (2017)

• Record Type: Book
• Further Information: Note: Valery Serov.
• Authors: Serov, V. S (Valeriĭ Sergeevich)
• Contents: Part I: Fourier Series and the Discrete Fourier Transform -- Introduction -- Formulation of Fourier Series -- Fourier Coefficients and their Properties -- Convolution and Parseval Equality -- Fejer Means of Fourier Series: Uniqueness of the Fourier Series -- Riemann-Lebesgue Lemma -- Fourier Series of Square-Integrable Function: Riesz-Fischer Theorem -- Besov and Holder Spaces -- Absolute Convergence: Bernstein and Peetre Theorems -- Dirichlet Kernel: Pointwise and Uniform Congergence -- Formulation of Discrete Fourier Transform and its Properties -- Connection Between the Discrete Fourier Transform and the Fourier Transform -- Some Applications of Discrete Fourier Transform -- Applications to Solving Some Model Equations -- Part II: Fourier Transform and Distributions -- Introduction -- Fourier Transform in Schwartz Space -- Fourier Transform inLp(Rn);1 p 2 -- Tempered Distributions -- Convolutions in S and S 1 -- Sobolev Spaces -- Homogeneous Distributions -- Fundamental Solution of the Helmholtz Operator -- Estimates for Laplacian and Hamiltonian -- Part III: Operator Theory and Integral Equations -- Introduction -- Inner Product Spaces and Hilbert Spaces -- Symmetric Operators in Hilbert Spaces -- J. von Neumann's Spectral Theorem -- Spectrum of Self-Adjoint Operators -- Quadratic Forms: Freidrich's Extension -- Elliptic Differential Operators -- Spectral Function -- Schrodinger Operator -- Magnetic Schrodinger Operator -- Integral Operators with Weak Singularities: Integral Equations of the First and Second Kind -- Volterra and Singular Integral Equations -- Approximate Methods -- Part IV: Partial Differential Equations -- Introduction -- Local Existence Theory -- The Laplace Operator -- The Dirichlet and Neumman Problems -- Layer Potentials -- Elliptic Boundary Value Problems -- Direct Scattering Problem for Helmholtz Equation -- Some Inverse Scattering Problems for the Schrodinger Operator -- The Heat Operator -- The Wave Operator.
• Publisher Details: Cham : Springer
• Publication Date: 2017
• Copyright Date: 2017
• Extent: 1 online resource (534 pages)
• Subjects: 515.2433 (S); Mathematics; Mathematical physics; Fourier series; Fourier transformations; Fourier transformations; Fourier series; Mathematical physics; Science -- Mathematical Physics; Mathematics -- Differential Equations; Mathematical physics; Differential calculus & equations; Fourier analysis; Differential equations, partial; Mathematics -- Mathematical Analysis; Functional analysis & transforms
• Languages: English
• ISBNs: 9783319652627
• Related ISBNs: 9783319652610
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.