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| Ïîèñê ïî óêàçàòåëÿì |
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| Lighthill M. J. — Introduction to Fourier analysis and generalized functions |
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| Ïðåäìåòíûé óêàçàòåëü |
Absolutely integrable 2 31—4 46—56
Absolutely integrable in every finite interval 48—56
Arbitrary constant in definitions of particular generalised functions 39—43
Asymptotic estimation 10
Asymptotic estimation of Fourier coefficients 75
Asymptotic estimation of Fourier transforms 46—57
Asymptotic expansion 50 54—7
Bessel functions 50—1 53—7
boundary conditions 4—5 9
Cauchy principal value 14 37—8
Classical theory, of Fourier series 7 60 66
Classical theory, of Fourier transforms 8—9 34
Constant generalised function 17
Constant, arbitrary, in definitions of particular generalised functions 39—43
Contour integration 2 33 44
Convergence of Fourier series 6—7 58—60
Delta function 1 9—13 33 25—9 31 36—41 48
Delta function, definition of 17
Delta function, derivatives of 11—13 19 36—7 29 32 36 39 43—5 52 61 68
Differential equation 1 3—10
Differentiation, of generalised function 18 24—5
Differentiation, of series term by term 3—4 7 29 59 68—9
Differentiation, with respect to a parameter 39 34—5
Dipole 13
Dirac, P. A. M., i 9—10
Elliptic function 70
Equivalent regular sequences 17
Error term 46 53
Error term, precise order of magnitude of 55 7 74—5
Even function 5—7 10 26—7 31 38 41
Factorial function 33—6 51 53—4
Fairly good function 15 18—20 38—9 65 72
Fourier coefficients 3—7 60—75
Fourier coefficients, asymptotic estimation of 71—5
Fourier cosine integral 10 56—7
Fourier cosine series 5 7 68—71 75
Fourier inversion theorem, for generalised functions 20
Fourier inversion theorem, for good functions 16
Fourier inversion theorem, for particular generalised functions 34 40—4
Fourier series 1 3—7 58—75
Fourier series, classical theory of 7 60 66
Fourier series, convergence of 6—7 58 60
Fourier series, differentiation of 3—4 7 29 67—9
Fourier series, existence of, for any periodic generalised function 62—6
Fourier series, half-range, quarter-range 4—7 74—5
Fourier series, summability of 14 68
Fourier series, uniqueness of representation by 4 7 58 60 68
Fourier sine integral 9 56—7
Fourier sine series 5 7 68 74—5
Fourier transform (f.t.) 8 10
Fourier transform (f.t.) of derivative of generalised function 30 33
Fourier transform (f.t.) of generalised function 18—21 34 27
Fourier transform (f.t.) of good function 15—16
Fourier transform (f.t.) of ordinary function 24
Fourier transform (f.t.) of particular generalised functions 30—45
Fourier transform (f.t.) of periodic function 58—68
Fourier transform (f.t.) of rational function 42—5
Fourier transform (f.t.), asymptotic estimation of 1
Fourier transform (f.t.), classical theory of 8—9 24
Fourier transform (f.t.), definitions of 8 15 18
Fourier transform (f.t.), limit of 28—9 36 40—1
Fourier transform (f.t.), summary of results on 42—5
Fourier transform (f.t.), table of 43
frequency 8 49
Generalised function 1 10—14
Generalised function derivative of with respect to a parameter 29 34—5
Generalised function, constant 17
Generalised function, definition of 17
Generalised function, derivative of, J 8 34—5
Generalised function, equal to ordinary function in an interval 35—6
Generalised function, general properties 16—29
Generalised function, limit of 27—9
Generalised function, limit of derivative of 28—9 33 39
Generalised function, limit of F.T. of 28—9 36 40—1
Generalised function, ordinary function as 21—4
Generalised function, particular 30—45 53—7
Generalised function, periodic 60—75
| Generalised function, series of 29 58—75
Generalised function, well behaved at infinity 49—57 73
Good function 13—16
Good function, definition of 15
Good function, fairly 15 18—20 28—9 65 72
Good function, sequence of 10—14 16—18 21—3 65—6 70
Hadamard finite part 14 31—2 34
Half-range, Fourier integral 9—10 56—7
Half-range, Fourier series 4—7 74—5
Hardy, G. H. 7
Heaviside unit function H(x) 30—45 55—8 69
Historical account of subject 13
Improper integral 31—2 37—8
Indefinite integral 14 38
Integral powers 35—40
Integral powers, multiplied by logarithms 40—2
Integration byparts 11 15 19 31—2 37
Interchange of order, of limit processes and differentiation 8 9 35
Interchange of order, of limit processes and Fourier transformation 38—9 36 40—1
Interchange of order, of summation and/or integration 2 16 22—4 59 64—6
Jacobi’s transformation 70
Laplace’s equation 3—4
Laurent’s theorem 4
Lebesgue theory of integration 2
Limit, of derivatives of generalised functions 28—9 33 39
Limit, of f.t.’s of generalised functions 28—9 36 40—1
Limit, of generalised functions 27—9
Logarithmic singularities 34—5 40—3 52 56—7 75
Mikusfnski, J. G. 13
Non-integral powers 30—4
Odd function 5—7 9 26—7 31 36
Ordinary function, as generalised function 21—4
Ordinary function, derivative of 23—5
Ordinary function, equal to generalised function in an interval 25—6
oscillations 3 8 49
Parseval’s theorem 16 19 69
Partial fractions 42—5
Particular generalised functions 30 45 53—7
Particular generalised functions, arbitrary constant in definition of 39—43
Periodic function 3—7
Periodic function, equal to given function in an interval 5—6 8 69
Periodic function, generalised 60 75
Point charge 12
Poisson summation formula 67—71
Polar coordinates 3—4
Powers, integral 35—40
Powers, non-integral 30—4
Psi function (a) 35 39—43
Quarter-range Fourier series 4—6
Rational function, F.T. of 42—5
Regular sequence 16—18 21—3 65—6
Remainder 46 52
Riemann — Lebesgue lemma 46—51
Rogosinski, W. W. 7
Row of delta functions, i 60 67—9
Schwartz, L., I 14
Sequence of good functions 10—14 16—18 21—3 65—6
Series of generalised functions 29 58—75
Sgn function 23 28 30—45 47 49 52 54 56—7 72 74
Singularity 42 51—7 72—5
Singularity, defined 51 72
Singularity, worst 55 57 75
Smudge function 22
Step function 58—9
String, plucked 5—6
Summability of Fourier series 14 68
Summary of Fourier transform results 42—45
Temple. G. 1 8 13—14
Test function 13—14
Theta function 70
Titchmarsh, E. C. 8
Unitary function 61—7 71—3
Watson, G. N. 51
wave number 8
Waveform 3
Well behaved at infinity 49—57 73
“Worst” singularity 55 57 75
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