2010/01/01 by J. J. Duistermaat, J. A. C. Kolk, J. P. van Braam Houckgeest · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Applied mathematics #Arithmetic #Calculus (dental) #Computer science #Convolution (computer science) #Discrete mathematics #Fourier series #Fourier transform #Fractional Differential Equations Solutions #Mathematical analysis #Mathematical and Theoretical Analysis #Mathematical economics #Mathematics #Nonlinear Partial Differential Equations #Notation #Peano axioms #Rational number #Sobolev space
paper · doi:10.1007/978-0-8176-4675-2
openalex publication_date 2010/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Preface.- Standard Notation.- 1 Motivation .- Problems.- 2 Test Functions.- Problems.- 3 Distributions.- Problems.- 4 Differentiation of Distributions.- Problems.- 5 Convergence of Distributions.- Problems.- 6 Taylor Expansion in Several Variables.- Problems.- 7 Localization.- Problems.- 8 Distributions with Compact Support.- Problems.- 9 Multiplication by Functions.- Problems.- 10 Transposition: Pullback and Pushforward.- Problems.- 11 Convolution of Distributions.- Problems.- 12 Fundamental Solutions.- Problems.- 13 Fractional Integration and Differentiation .- 13.1 The Case of Dimension One.- 13.2 Wave Family.- 13.3 Appendix: Euler's Gamma Function.- Problems.- 14 Fourier Transform.- Problems.- 15 Distribution Kernels.- Problems.- 16 Fourier Series.- Problems.- 17 Fundamental Solutions and Fourier Transform.- 17.1 Appendix: Fundamental Solution of .I?/k.- Problems.- 18 Supports and Fourier Transform.- Problems.- 19 Sobolev Spaces.- Problems.- 20 Appendix: Integration.- 21 Solutions to Selected Problems.- References.- Index of Notation.- Index.