Titre :	Integral transforms in lp spaces : course and corrected exercises
Type de document :	document électronique
Auteurs :	Khalouta,Ali, Auteur
Editeur :	Setif:UFA
Année de publication :	2025
Importance :	1 vol (99 f .)
Langues :	Anglais (eng)
Catégories :	Publications pédagogiques:Mathématiaue P/P
Mots-clés :	Lp Spaces Fourier transform Laplace transform.
Index. décimale :	510 Mathématique
Résumé :	This pedagogical handout is the course material for "Integral transforms in Lp Spaces," taught by Dr. Ali KHALOUTA to third-year students licence in mathematics at Ferhat ABBAS University Setif 1. Developed throughout the year, this document does not replace the course. It closely follows the lectures, with only minor modifications, it reproduces the course exactly as it was given to all students.
Note de contenu :	Table of contents Introductioniv 1 Lp spaces1 1.1Someintegrationresults............................. 1 1.2 Lp spaces:deÂ…nitionsandproperties...................... 3 1.3Re‡exibility,Separability,andDualityof Lp . ................. 9 1.3.1Re‡exivity................................. 9 1.3.2Separability................................ 11 1.3.3Duality.................................. 12 1.4Convolutionandregularizationon Rn . ..................... 13 1.4.1Supportsinconvolution......................... 17 1.4.2Regularizingsequences.......................... 21 1.5Correctedexercises................................ 24 1.6Suggestedexercises................................ 32 2 Fouriertransform34 2.1Fouriertransformforintegrablefunctions.................... 34 2.2CosineandSine-Fouriertransforms....................... 38 2.3PropertiesofFouriertransform......................... 39 2.3.1Linearity.................................. 39 2.3.2Complexconjugation........................... 39 2.3.3Translation................................ 40 2.3.4Changeofscale.............................. 40 2.3.5Modulation................................ 41 2.3.6Convolution................................ 41 2.3.7Fouriertransformofthederivativeofafunction............ 42 2.3.8DerivationoftheFouriertransform................... 43 2.4InverseFouriertransform............................. 44 2.5Fouriertransformforsquare-summablefunctions................ 46 2.6Applications.................................... 48 2.6.1Ordinarydi¤erentialequations...................... 48 2.6.2Partialdi¤erentialequations....................... 50 2.7Fouriertransformofusuelfunctions....................... 52 2.8Correctedexercises................................ 52 2.9Suggestedexercises................................ 66 3 Laplacetransform68 3.1DeÂ…nitionandexistenceoftheLaplacetransform............... 68 3.2ExamplesofLaplacetransformofelementaryfunctions............ 70 3.3PropertiesoftheLaplacetransform....................... 71 3.3.1Linearity.................................. 71 3.3.2Translationofthevariable t (DelayTheorem)............. 73 3.3.3Translationofthevariable p (Modulation)............... 74 3.3.4Changeofscale.............................. 75 3.3.5Complexconjugation........................... 75 3.3.6Laplacetransformofaderivative.................... 76 3.3.7Generalizationtohigherderivatives................... 77 3.3.8DerivationoftheLaplacetransform................... 77 3.3.9Laplacetransformofintegrals...................... 79 3.3.10Laplacetransformofaperiodicfunction................ 80 3.3.11Laplacetransformofconvolution.................... 80 3.4InverseLaplacetransform............................ 81 3.5Laplacetransformofusuelfunctions...................... 82 3.6Applicationtosolvingofdi¤erentialequations................. 83 3.6.1Solvinglineardi¤erentialequationswithconstantcoe¢cients..... 83 3.7Correctedexercises................................ 86 3.8Suggestedexercises................................ 97
Côte titre :	PM/0049
En ligne :	http://dspace.univ-setif.dz:8888/jspui/bitstream/123456789/6657/1/1-Polycopi%c3% [...]

Integral transforms in lp spaces : course and corrected exercises [document électronique] / Khalouta,Ali, Auteur . - [S.l.] : Setif:UFA, 2025 . - 1 vol (99 f .).
Langues : Anglais (eng)

Catégories :	Publications pédagogiques:Mathématiaue P/P
Mots-clés :	Lp Spaces Fourier transform Laplace transform.
Index. décimale :	510 Mathématique
Résumé :	This pedagogical handout is the course material for "Integral transforms in Lp Spaces," taught by Dr. Ali KHALOUTA to third-year students licence in mathematics at Ferhat ABBAS University Setif 1. Developed throughout the year, this document does not replace the course. It closely follows the lectures, with only minor modifications, it reproduces the course exactly as it was given to all students.
Note de contenu :	Table of contents Introductioniv 1 Lp spaces1 1.1Someintegrationresults............................. 1 1.2 Lp spaces:deÂ…nitionsandproperties...................... 3 1.3Re‡exibility,Separability,andDualityof Lp . ................. 9 1.3.1Re‡exivity................................. 9 1.3.2Separability................................ 11 1.3.3Duality.................................. 12 1.4Convolutionandregularizationon Rn . ..................... 13 1.4.1Supportsinconvolution......................... 17 1.4.2Regularizingsequences.......................... 21 1.5Correctedexercises................................ 24 1.6Suggestedexercises................................ 32 2 Fouriertransform34 2.1Fouriertransformforintegrablefunctions.................... 34 2.2CosineandSine-Fouriertransforms....................... 38 2.3PropertiesofFouriertransform......................... 39 2.3.1Linearity.................................. 39 2.3.2Complexconjugation........................... 39 2.3.3Translation................................ 40 2.3.4Changeofscale.............................. 40 2.3.5Modulation................................ 41 2.3.6Convolution................................ 41 2.3.7Fouriertransformofthederivativeofafunction............ 42 2.3.8DerivationoftheFouriertransform................... 43 2.4InverseFouriertransform............................. 44 2.5Fouriertransformforsquare-summablefunctions................ 46 2.6Applications.................................... 48 2.6.1Ordinarydi¤erentialequations...................... 48 2.6.2Partialdi¤erentialequations....................... 50 2.7Fouriertransformofusuelfunctions....................... 52 2.8Correctedexercises................................ 52 2.9Suggestedexercises................................ 66 3 Laplacetransform68 3.1DeÂ…nitionandexistenceoftheLaplacetransform............... 68 3.2ExamplesofLaplacetransformofelementaryfunctions............ 70 3.3PropertiesoftheLaplacetransform....................... 71 3.3.1Linearity.................................. 71 3.3.2Translationofthevariable t (DelayTheorem)............. 73 3.3.3Translationofthevariable p (Modulation)............... 74 3.3.4Changeofscale.............................. 75 3.3.5Complexconjugation........................... 75 3.3.6Laplacetransformofaderivative.................... 76 3.3.7Generalizationtohigherderivatives................... 77 3.3.8DerivationoftheLaplacetransform................... 77 3.3.9Laplacetransformofintegrals...................... 79 3.3.10Laplacetransformofaperiodicfunction................ 80 3.3.11Laplacetransformofconvolution.................... 80 3.4InverseLaplacetransform............................ 81 3.5Laplacetransformofusuelfunctions...................... 82 3.6Applicationtosolvingofdi¤erentialequations................. 83 3.6.1Solvinglineardi¤erentialequationswithconstantcoe¢cients..... 83 3.7Correctedexercises................................ 86 3.8Suggestedexercises................................ 97
Côte titre :	PM/0049
En ligne :	http://dspace.univ-setif.dz:8888/jspui/bitstream/123456789/6657/1/1-Polycopi%c3% [...]