Конволуција

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Конволуција функција f_1,\;f_2\, је функција

\phi(x)=\int_{-\infty}^{+\infty}f_1(x-y)f_2(y)\,dy.

Конволуција функција се често означава са \phi=f_1*f_2\,.

Примери појављивања

Литература[уреди]

  • Bracewell, R. (1986). The Fourier Transform and Its Applications (2nd ed.). McGraw–Hill. ISBN 0071160434. .
  • Hewitt Edwin, Ross Kenneth A. (1979). Abstract harmonic analysis. Vol. I. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. 115 (2nd ed.). Berlin, New York: Springer-Verlag. ISBN 978-3-540-09434-0. MR 551496. .
  • Hewitt Edwin, Ross Kenneth A. (1970). Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups. Die Grundlehren der mathematischen Wissenschaften, Band 152. Berlin, New York: Springer-Verlag. MR 0262773. .
  • The analysis of linear partial differential operators I. Grundl. Math. Wissenschaft.. 256. Springer. 1983. MR 0717035. ISBN 3-540-12104-8. .
  • Kassel Christian (1995). Quantum groups. Graduate Texts in Mathematics. 155. Berlin, New York: Springer-Verlag. ISBN 978-0-387-94370-1. MR 1321145. .
  • Donald Knuth (1997). Seminumerical Algorithms (3rd. ed.). Reading, Massachusetts: Addison–Wesley. ISBN 0-201-89684-2. .
  • Rudin Walter (1962). Fourier analysis on groups. Interscience Tracts in Pure and Applied Mathematics, No. 12. Interscience Publishers (a division of John Wiley and Sons), New York–London. MR 0152834. ISBN 047152364X. .
  • Elias Stein, Guido Weiss (1971). Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press. ISBN 0-691-08078-X. .
  • R. Strichartz (1994). A Guide to Distribution Theory and Fourier Transforms. CRC Press. ISBN 0849382734. .
  • Titchmarsh Edward (1948). Introduction to the theory of Fourier integrals (2nd ed.). New York, N.Y.: Chelsea Pub. Co. (published 1986). ISBN 978-0828403245. .
  • Uludag A. M. (1998). „On possible deterioration of smoothness under the operation of convolution“. J. Math. Anal. Appl. 227 no. 2, 335–358. 
  • François Treves (1967). Topological Vector Spaces, Distributions and Kernels. Academic Press. ISBN 0486453529. .
  • von zur Gathen, J.; Gerhard, J. (2003). Modern Computer Algebra. Cambridge University Press. ISBN 0-521-82646-2. .
  • Diggle P. J. (1995). „A kernel method for smoothing point process data“. Journal of the Royal Statistical Society, Series C) 34 (1985) 138–147. 

Спољашње везе[уреди]