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Lighthill M. J. Ч Introduction to Fourier analysis and generalized functions
Lighthill M. J. Ч Introduction to Fourier analysis and generalized functions

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Ќазвание: Introduction to Fourier analysis and generalized functions

јвтор: Lighthill M. J.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1964

 оличество страниц: 87

ƒобавлена в каталог: 28.10.2012

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Absolutely integrable      2 31Ч4 46Ч56
Absolutely integrable in every finite interval      48Ч56
Arbitrary constant in definitions of particular generalised functions      39Ч43
Asymptotic estimation      10
Asymptotic estimation of Fourier coefficients      75
Asymptotic estimation of Fourier transforms      46Ч57
Asymptotic expansion      50 54Ч7
Bessel functions      50Ч1 53Ч7
boundary conditions      4Ч5 9
Cauchy principal value      14 37Ч8
Classical theory, of Fourier series      7 60 66
Classical theory, of Fourier transforms      8Ч9 34
Constant generalised function      17
Constant, arbitrary, in definitions of particular generalised functions      39Ч43
Contour integration      2 33 44
Convergence of Fourier series      6Ч7 58Ч60
Delta function      1 9Ч13 33 25Ч9 31 36Ч41 48
Delta function, definition of      17
Delta function, derivatives of      11Ч13 19 36Ч7 29 32 36 39 43Ч5 52 61 68
Differential equation      1 3Ч10
Differentiation, of generalised function      18 24Ч5
Differentiation, of series term by term      3Ч4 7 29 59 68Ч9
Differentiation, with respect to a parameter      39 34Ч5
Dipole      13
Dirac, P. A. M., i      9Ч10
Elliptic function      70
Equivalent regular sequences      17
Error term      46 53
Error term, precise order of magnitude of      55 7 74Ч5
Even function      5Ч7 10 26Ч7 31 38 41
Factorial function      33Ч6 51 53Ч4
Fairly good function      15 18Ч20 38Ч9 65 72
Fourier coefficients      3Ч7 60Ч75
Fourier coefficients, asymptotic estimation of      71Ч5
Fourier cosine integral      10 56Ч7
Fourier cosine series      5 7 68Ч71 75
Fourier inversion theorem, for generalised functions      20
Fourier inversion theorem, for good functions      16
Fourier inversion theorem, for particular generalised functions      34 40Ч4
Fourier series      1 3Ч7 58Ч75
Fourier series, classical theory of      7 60 66
Fourier series, convergence of      6Ч7 58 60
Fourier series, differentiation of      3Ч4 7 29 67Ч9
Fourier series, existence of, for any periodic generalised function      62Ч6
Fourier series, half-range, quarter-range      4Ч7 74Ч5
Fourier series, summability of      14 68
Fourier series, uniqueness of representation by      4 7 58 60 68
Fourier sine integral      9 56Ч7
Fourier sine series      5 7 68 74Ч5
Fourier transform (f.t.)      8 10
Fourier transform (f.t.) of derivative of generalised function      30 33
Fourier transform (f.t.) of generalised function      18Ч21 34 27
Fourier transform (f.t.) of good function      15Ч16
Fourier transform (f.t.) of ordinary function      24
Fourier transform (f.t.) of particular generalised functions      30Ч45
Fourier transform (f.t.) of periodic function      58Ч68
Fourier transform (f.t.) of rational function      42Ч5
Fourier transform (f.t.), asymptotic estimation of      1
Fourier transform (f.t.), classical theory of      8Ч9 24
Fourier transform (f.t.), definitions of      8 15 18
Fourier transform (f.t.), limit of      28Ч9 36 40Ч1
Fourier transform (f.t.), summary of results on      42Ч5
Fourier transform (f.t.), table of      43
frequency      8 49
Generalised function      1 10Ч14
Generalised function derivative of with respect to a parameter      29 34Ч5
Generalised function, constant      17
Generalised function, definition of      17
Generalised function, derivative of, J      8 34Ч5
Generalised function, equal to ordinary function in an interval      35Ч6
Generalised function, general properties      16Ч29
Generalised function, limit of      27Ч9
Generalised function, limit of derivative of      28Ч9 33 39
Generalised function, limit of F.T. of      28Ч9 36 40Ч1
Generalised function, ordinary function as      21Ч4
Generalised function, particular      30Ч45 53Ч7
Generalised function, periodic      60Ч75
Generalised function, series of      29 58Ч75
Generalised function, well behaved at infinity      49Ч57 73
Good function      13Ч16
Good function, definition of      15
Good function, fairly      15 18Ч20 28Ч9 65 72
Good function, sequence of      10Ч14 16Ч18 21Ч3 65Ч6 70
Hadamard finite part      14 31Ч2 34
Half-range, Fourier integral      9Ч10 56Ч7
Half-range, Fourier series      4Ч7 74Ч5
Hardy, G. H.      7
Heaviside unit function H(x)      30Ч45 55Ч8 69
Historical account of subject      13
Improper integral      31Ч2 37Ч8
Indefinite integral      14 38
Integral powers      35Ч40
Integral powers, multiplied by logarithms      40Ч2
Integration byparts      11 15 19 31Ч2 37
Interchange of order, of limit processes and differentiation      8 9 35
Interchange of order, of limit processes and Fourier transformation      38Ч9 36 40Ч1
Interchange of order, of summation and/or integration      2 16 22Ч4 59 64Ч6
JacobiТs transformation      70
LaplaceТs equation      3Ч4
LaurentТs theorem      4
Lebesgue theory of integration      2
Limit, of derivatives of generalised functions      28Ч9 33 39
Limit, of f.t.Тs of generalised functions      28Ч9 36 40Ч1
Limit, of generalised functions      27Ч9
Logarithmic singularities      34Ч5 40Ч3 52 56Ч7 75
Mikusfnski, J. G.      13
Non-integral powers      30Ч4
Odd function      5Ч7 9 26Ч7 31 36
Ordinary function, as generalised function      21Ч4
Ordinary function, derivative of      23Ч5
Ordinary function, equal to generalised function in an interval      25Ч6
oscillations      3 8 49
ParsevalТs theorem      16 19 69
Partial fractions      42Ч5
Particular generalised functions      30 45 53Ч7
Particular generalised functions, arbitrary constant in definition of      39Ч43
Periodic function      3Ч7
Periodic function, equal to given function in an interval      5Ч6 8 69
Periodic function, generalised      60 75
Point charge      12
Poisson summation formula      67Ч71
Polar coordinates      3Ч4
Powers, integral      35Ч40
Powers, non-integral      30Ч4
Psi function (a)      35 39Ч43
Quarter-range Fourier series      4Ч6
Rational function, F.T. of      42Ч5
Regular sequence      16Ч18 21Ч3 65Ч6
Remainder      46 52
Riemann Ч Lebesgue lemma      46Ч51
Rogosinski, W. W.      7
Row of delta functions, i      60 67Ч9
Schwartz, L., I      14
Sequence of good functions      10Ч14 16Ч18 21Ч3 65Ч6
Series of generalised functions      29 58Ч75
Sgn function      23 28 30Ч45 47 49 52 54 56Ч7 72 74
Singularity      42 51Ч7 72Ч5
Singularity, defined      51 72
Singularity, worst      55 57 75
Smudge function      22
Step function      58Ч9
String, plucked      5Ч6
Summability of Fourier series      14 68
Summary of Fourier transform results      42Ч45
Temple. G.      1 8 13Ч14
Test function      13Ч14
Theta function      70
Titchmarsh, E. C.      8
Unitary function      61Ч7 71Ч3
Watson, G. N.      51
wave number      8
Waveform      3
Well behaved at infinity      49Ч57 73
УWorstФ singularity      55 57 75
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