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Vladimirov V. S. — Equations of mathematical physics
Vladimirov V. S. — Equations of mathematical physics

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Название: Equations of mathematical physics

Автор: Vladimirov V. S.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1971

Количество страниц: 426

Добавлена в каталог: 16.11.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Arzela's lemma      233
Associated Legendre functions      339
Bessel's inequality      17
Bilinear expansion of an Hermitian continuous kernel      242
Bilinear expansion of iterated kernels      241
Bilinear form      25
Bolzano — Weierstrass theorem      2
Boundary value problem      53
Boundary value problem for equations of elliptic type      56
Cauchy principle of convergence      2
Cauchy — Buniakowski inequality      12
Cauchy's problem      53
Cauchy's theorem      5
Characteristic cone      43
Characteristic equation      43
Characteristic function of a set      2
Characteristic numbers of a kernel      202
Characteristic surface      43
Closure equation      17
Closure of a set      2
Compactum      2
Complete system of functions      17
Continuation of a linear functional      21
Continuity, equation of      35
Convolution of generalized functions      102 104 105
Convolution of generalized functions of slow growth      121
d'Alembert's formula      176
Derivative of a generalized function      80
Derivative, correct normal      281
Descent, method of      144
Differential equations of characteristics      47
Diffusion equation      30
Diffusion of heat in a bounded rod      382
Dini's lemma      5
Dirac $\delta$-function      64
Dirac's equation      38
Direct product of generalized functions      96
Direct product of generalized functions of slow growth      96
Dirichlet, external problem      307
Dirichlet, internal problem      307
Distributions      75
Du Bois Reymond's Lemma      72
Eigenfunctions of a kernel      202
Eigenfunctions of an operator      24
Eigenvalues of a kernel      202
Eigenvalues of an operator      24
Elliptic equation      380
Elliptic type, equation of      40 49
Energy integral      259
Euler's equation of motion      35
Fourier coefficients      16
Fourier method      263 373
Fourier series      16
Fourier transform of convolution      129
Fourier transform of functions belonging to $\mathscr{S}$      121
Fourier transform of generalized functions belonging to $\mathscr{S}'$      123
Fredholm integral equations      201
Fredholm integral equations, adjoint      201
Fredholm integral equations, homogeneous      201
Fredholm theorems      225—227 229 233
Fredholm's alternative      225
Fubini's theorem      11
Function with compact support      4
Functional, linear      21
Fundamental solution      141 147
Fundamental solution of the Cauchy — Riemann operator      154
Fundamental solution of the heat conduction operator      148
Fundamental solution of the Helmholtz operator      153
Fundamental solution of the Laplace operator      151
Fundamental solution of the transport operator      154
Fundamental solution of the wave operator      149
Generalized Cauchy problem for heat conduction equation      197
Generalized Cauchy problem for wave equation      172
Generalized function      69
Generalized function of slow growth      116
Generalized function, regular      72
Generalized function, singular      72
Generalized harmonic function      287
Generalized solution of linear differential equation      140
Generating function for Legendre polynomials      337
Green's first formula      256
Green's formula      279
Green's function of a boundary value problem      274
Green's function of a Dirichlet problem      318 358
Green's function of an operator      273
Green's function, construction      322
Green's second formula      257
Hadamard's example      60
Harmonic function      278
Heat conduction equation      31 44
Heine — Borel lemma      3
Helmholtz equation      33 362
Helmholtz equation, homogeneous      363
Hilbert — Schmidt theorem      237 240 247 249
Hoelder continuous function      5
Huygens principle      179
Hydrodynamics, equations of      35
Hyperbolic homogeneous equation      374
Hyperbolic inhomogeneous equation      376
Hyperbolic type equations      40 46
Influence, function of      141
Integral equation      201
Integral equation with degenerate kernel      217
Integral equation with Hermitian kernel      202
Integral equation with polar kernel      211
Integral equation, Fredholm      201
Integral equation, Volterra      209
Interior point of a set      2
Iterates of a function      204
Jentsch's theorem      249
Kellogg's method      251
Kelvin's transformation      309
Kernel      21
Kernel of integral equation      201
Kernel of positive type      246
kernel, continuous      202
Kernel, degenerate      217
kernel, hermitian      231
Kernel, polar      211
Kernel, Volterra      209
Kernel, weakly polar      211
Kernels, Hermitian adjoint      202
Kernels, iterated      206
Kernels, symmetric      249
Kirchhoff's formula      176
Klein — Gordon equation      38
Kowalewski's theorem      59
Laplace equation      33
Laplace's formula      343
Lebesgue integrable function      5 6
Lebesgue integral      5 6
Lebesgue theorem      8
Legendre polynomials      335
Liapunov surface      297
Linear normed space      4
Lipschitz continuous function      5
Maximum principle      283 285 405
Maxwell's equations      36
Mean value theorem      283
Measurable function      6
Minimum principle      406
Mixed problem      54 57
Mixed type, equation of      41
Multiplicity of an eigenvalue      24
Neumann series      204
Neumann, external problem      307
Neumann, internal problem      307
Normalized function      15
Normally hyperbolic type equation      40
Normally parabolic type equation      40
Operator, bounded from $\mathscr{M}$ to $\mathscr{N}$      20
Operator, Cauchy — Riemann      94
Operator, continuous from $\mathscr{M}$ to $\mathscr{N}$      20
Operator, differential, or order m      22
Operator, Hermitian (Lagrange self-adjoint)      25
Operator, integral      21
Operator, integrodi\taufferential      22
Operator, Laplace $\Delta$      30
Operator, linear      20
Operator, positive      26
Operator, wave (D'Alembert $\Box_{a}$)      30
Orthogonal functions      15
Orthonormal system of functions      15
Parabolic type equations      40 49 378
Parseval's equality      17
Poisson's equation      33 44
Poisson's formula      186 325 326
Potential, double layer      111 293 302 303
Potential, heat with density f      194
Potential, logarithmic      110 350
Potential, Newtonian      110 291
Potential, Newtonian, physical sense      296
Potential, retarded      163
Potential, Robin's      316
Potential, Robin's, physical sense      317
Potential, simple layer      111 293 300 304
Potential, surface retarded      167
Potentials      365
Principle of amplitude      369
Principle of limiting absorption      368
Propagation of waves      178
Property fulfilled almost everywhere      5
Quadratic form      25
Reflections, finite string      191
Reflections, method of      322
Reflections, semi-infinite string      198
Region      3
Regularization of generalized functions      108
Resolvent      207
Riesz — Fischer theorem      14
Schmidt's formula      244
Schmidt's orthogonalization process      16
Schrodinger's Equation      37 379
Schwartz's Theorem      115
Sequence in itself      2
Sequence of functions, converging in the mean      13
Sequence, converging      2
Set of functions continuous in $\mathscr{L}_{2}(G)$      13
Set of measure zero      6
Set, bounded      2
Set, closed      2
Set, connected      2
Set, equicontinuous functions      5
Set, measurable      6
Set, open      2
Small longitudinal vibrations of a rod      29
Small transverse vibrations of a membrane      30
Small transverse vibrations of a string      29
Sokhotski's formula      75
Sommerfeld radiation conditions      362
Space, $C^{p}$, $p\geq1$      3
Space, $C^{p}(G)$      3
Space, $C^{p}(\overline{G})$      3
Space, $\mathscr{D}$      66
Space, $\mathscr{D}'$      69
Space, $\mathscr{D}(G)$      4
Space, $\mathscr{L}$      113
Space, $\mathscr{L}'$      114
Space, $\mathscr{L}_{2}(G)$      12
Space, C(T), T closed      4
Spherical function      333 345
State, equation of      35
Steklov's theorem      277
Sturm — Liouville problem      270
Sufficiently-smooth surface      310
Summable function      6 8
Superposition of waves, principle of      179
Support of a generalized function      70
Support of a piecewise continuous function      4
Telegrapher's equation      36
Test functions      63 65 113
Transformation, Fourier, of convolution      129
Transformation, Fourier, of the function belonging to $\mathscr{L}$      121
Transformation, Fourier, of the generalized function belonging to $\mathscr{L}'$      123
Transport equation      33
Tricomi's equation      41 51
Types of equations      40
Vibration equations      27
Vibration of a fixed membrane      383
Vibration of a spherical volume      384
Vibration of a string      381
Wave equation      29
Weak convergence      70
Weierstrass theorem      5
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