Конволуција — разлика између измена

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Тренутна верзија на датум 7. април 2024. у 16:03

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

Bracewell, R. (1986). „The Fourier Transform and Its Applications” (2nd изд.). McGraw–Hill. ISBN 9780071160438. .
Hewitt Edwin, Ross Kenneth A. (1979). Abstract harmonic analysis. Vol. I. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. 115 (2nd изд.). 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. ISBN 978-3-540-12104-6. MR 0717035. Непознати параметар |autghor= игнорисан (помоћ).
Christian, Kassel (1995). Quantum groups. Graduate Texts in Mathematics. 155. Berlin, New York: Springer-Verlag. ISBN 978-0-387-94370-1. MR 1321145. .
Knuth, Donald (1997). Seminumerical Algorithms (3rd. изд.). Reading, Massachusetts: Addison–Wesley. ISBN 978-0-201-89684-8. .
Walter, Rudin (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. ISBN 9780471523642. MR 0152834. .
Elias Stein, Guido Weiss (1971). Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press. ISBN 978-0-691-08078-9. .
Strichartz, R. (1994). A Guide to Distribution Theory and Fourier Transforms. CRC Press. ISBN 9780849382734. .
Edward, Titchmarsh (1948). Introduction to the theory of Fourier integrals (2nd изд.). New York, N.Y.: Chelsea Pub. Co. (објављено 1986). ISBN 978-0828403245. .
M., Uludag A. (1998). „On possible deterioration of smoothness under the operation of convolution”. J. Math. Anal. Appl. 227 no. 2, 335–358.
Treves, François (1967). Topological Vector Spaces, Distributions and Kernels. Academic Press. ISBN 9780486453521. .
von zur Gathen, J.; Gerhard, J. (2003). Modern Computer Algebra. Cambridge University Press. ISBN 978-0-521-82646-4. .
J., Diggle P. (1995). „A kernel method for smoothing point process data”. Journal of the Royal Statistical Society, Series C) 34 (1985) 138–147.

Спољашње везе

@@ Ред 1: / Ред 1: @@
-'''Конволуција''' функција <math>f_1,\;f_2\,</math> је [[функција]]
+'''Конволуција''' функција <math>f_1,\;f_2\,</math> је [[Функција (математика)|функција]]
 : <math>\phi(x)=\int_{-\infty}^{+\infty}f_1(x-y)f_2(y)\,dy.</math>
 Конволуција функција се често означава са <math>\phi=f_1*f_2\,.</math>
 '''Примери појављивања'''
@@ Ред 12: / Ред 12: @@
 * [[Функционална анализа]].
+== Литература ==
+{{Литература|2}}
+* {{cite journal|last=Bracewell|first=R.| title=The Fourier Transform and Its Applications|url=https://archive.org/details/fouriertransform0000brac_v1d6| edition=2nd |
+publisher=McGraw–Hill |year=1986 |isbn=9780071160438|pages=}}.
+* {{Cite book|ref=harv|author=Hewitt Edwin, Ross Kenneth A. | title=Abstract harmonic analysis. Vol. I | publisher=Springer-Verlag | location=Berlin, New York | edition=2nd | series=Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] |isbn=978-3-540-09434-0 | mr=551496 |year=1979 | volume=115}}.
+* {{Cite book|ref=harv|author=Hewitt Edwin, Ross Kenneth A. | title=Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups | publisher=Springer-Verlag | location=Berlin, New York | series=Die Grundlehren der mathematischen Wissenschaften, Band 152 | mr=0262773 |year=1970}}.
+* {{Cite book|ref=harv|mr=0717035|autghor=L. Hörmander |title=The analysis of linear partial differential operators I|series= Grundl. Math. Wissenschaft. |volume= 256 |publisher= Springer  |year=1983|isbn=978-3-540-12104-6|pages=}}.
+* {{Cite book|ref=harv|last=Christian|first=Kassel| title=Quantum groups | publisher=Springer-Verlag | location=Berlin, New York | series=Graduate Texts in Mathematics |isbn=978-0-387-94370-1 | mr=1321145 |year=1995 | volume=155}}.
+* {{Cite book|ref=harv|last=Knuth|first=Donald|title=Seminumerical Algorithms|edition=3rd.|publication-place=Reading, Massachusetts|publisher=Addison–Wesley|year=1997|isbn=978-0-201-89684-8|pages=}}.
+* {{Cite book|ref=harv|last=Walter|first=Rudin| title=Fourier analysis on groups | publisher=Interscience Publishers (a division of John Wiley and Sons), New York–London | series=Interscience Tracts in Pure and Applied Mathematics, No. 12 | mr=0152834 |year=1962 |isbn=9780471523642|pages=}}.
+* {{Cite book|ref=harv|author=Elias Stein, Guido Weiss |title=Introduction to Fourier Analysis on Euclidean Spaces|url=https://archive.org/details/introductiontofo0000stei|publisher=Princeton University Press|year=1971|isbn=978-0-691-08078-9|pages=}}.
+* {{Cite book|ref=harv|last=Strichartz|first=R.|year=1994|title=A Guide to Distribution Theory and Fourier Transforms|publisher=CRC Press|isbn=9780849382734|pages=}}.
+* {{Cite book|ref=harv|last=Edward|first=Titchmarsh|title=Introduction to the theory of Fourier integrals|isbn=978-0828403245|year=1948|edition=2nd|publication-date=1986|publisher=Chelsea Pub. Co.|location=New York, N.Y.}}.
+* {{cite journal|last=M.|first=Uludag A. |title=On possible deterioration of smoothness under the operation of convolution|journal=J. Math. Anal. Appl.  227  no. 2, 335–358|year=1998}}
+* {{Cite book|ref=harv|last=Treves|first=François|title=Topological Vector Spaces, Distributions and Kernels|url=https://archive.org/details/topologicalvecto0000fran|publisher=Academic Press|year=1967|isbn=9780486453521|pages=}}.
+* {{Cite book|ref=harv|first=J.|last=von zur Gathen|first2=J.|last2=Gerhard|title=Modern Computer Algebra|isbn=978-0-521-82646-4|year=2003|publisher=Cambridge University Press}}.
+* {{cite journal|last=J.|first=Diggle P. |title=A kernel method for smoothing point process data|journal=Journal of the Royal Statistical Society, Series C) 34 (1985) 138–147|year=1995}}
+{{Литература крај}}
+== Спољашње везе ==
+{{Commonscat|Convolution}}
+{{нормативна контрола}}
 [[Категорија:Математика]]
+[[Категорија:Обрада слике]]
+[[Категорија:Фуријеова анализа]]