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| Berezanskii Ju. M. — Expansions in Eigenfunctions of Selfadjoint Operators (Translations of Mathematical Monographs Vol 17) |
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Название: Expansions in Eigenfunctions of Selfadjoint Operators (Translations of Mathematical Monographs Vol 17)
Автор: Berezanskii Ju. M.
Язык: 
Рубрика: Математика/
Статус предметного указателя: Готов указатель с номерами страниц
ed2k:
Год издания: 1968
Количество страниц: 821
Добавлена в каталог: 09.07.2014
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| Предметный указатель |
*-commutativity 611
Borel set 8
Borel set, measurability by 8
Boundary conditions for unbounded regions 202
Boundary conditions, adjoint 71
Boundary conditions, almost correct 84
Boundary conditions, correct 805
Boundary conditions, Dirichlet 113
Boundary conditions, local satisfaction of 93
Boundary conditions, normal 218
Boundary conditions, normal systems of 218
Boundary conditions, null 113
Boundary conditions, preservation of 91
Boundary conditions, real 740
Boundary conditions, removal of 71
Boundary conditions, selfadjoint 379
Boundary of a region 5
Boundary problem, adjoint 82 214
Boundary, piece of 5
Boundary, piecewise smooth 5
Caplygin's expression 299
Cauchy operator for difference equations 540
Cauchy problem 387
Cauchy problem, uniqueness of weak solutions 387
Characteristics, strong 74
Characteristics, weak 74
Closure of operators 10
Closure of operators, by continuity 10
Closure of sets 1
Codimension 212
Conormal 74
Convolution of a function 26
Covering 205
Covering condition 205
Deficiency subspaces and numbers 12
Derivative, generalized, in the sense of S.L. Sobolev 24
Difference equation, adjoint 712
Difference equation, determinate 516
Difference equation, indeterminate 516
Difference equation, ordinary 501 559 712
Difference operator 502 560 581 589
Differential expression 70
Differential expression, adjoint 23 70
Differential expression, elliptic 103
Differential expression, hyperbolic 395
Differential expression, hypoelliptic 455
Differential expression, positive 95
Differential expression, strongly Carleman 453
Differential expression, strongly elliptic 104
Differential expression, with positive Hermitian part 95
Differential expression, with quadratic form bounded below 95
Differential operator 79
Dirichlet system 218
Ehrling — Nirenberg inequality 20
Eigenfunctions, integral 347
eigenvalue problems 98 120 152
Eigenvector, generalized 332
Eigenvector, generalized, in case of equipment with nuclear spaces 342
Elliptic expression, regular 205
Elliptic expression, smoothness of solutions 161
Elliptic expression, smoothness of solutions, inside a region 164 168 172 174
Elliptic expression, smoothness of solutions, up to the boundary 178 253 257
Elliptic problems, Noetherian 214
Ellipticity, regular 122
Energy inequalities 69 80
Energy inequalities for elliptic expressions, and general boundary conditions 207
Energy inequalities for elliptic expressions, and negative norms 137
Energy inequalities for elliptic expressions, on finite functions 112
Energy inequalities for functions satisfying null boundary conditions 121 144
Energy inequalities for general differential expressions with constant coefficients 263
Energy inequalities for nonelliptic expressions 282
Equipment of a space 33 66
Equipment of a space, extension of 332
Extension of equipment 322
Extension of equipment, of positive definite functions, of one variable 666
Extension of equipment, of positive definite functions, of two variables 704
Extension, solvable 80
Extreme points of a convex set 516 537
Factorization of the operator I 36
Fourier transform 62 498
Fourier transform by eigenvalues of a selfadjoint operator 331 338
Fourier transform by eigenvectors to functions, of a difference operator 510 560 581 591
Fourier transform by eigenvectors to functions, of an ordinary differential operator 495
Fourier transform of a generalized function 443 444
Fourier transform, inverse 444
Frankel condition 306 307
Frankel problem 312
Fredholm property problems 99
Function of the first kind 676
Function of the second kind 677
Function, continuously differentiable up to the boundary 14
Function, convolution of 26
Function, exponentially convex 686 702
Function, exponentially convex, of several variables 702
Function, finite 14
Function, generalized 22
Function, generalized spectral 337
Function, locally bounded 3
Function, Nevanlinna 534
Function, positive definite 661 702 711
Function, positive definite, determinate problem of continuation of 666
Function, positive definite, elementary 610
Function, positive definite, indeterminate problem of continuation of 666
Function, positive definite, of one variable, extension of 666
Function, positive definite, of several variables 701
Function, positive definite, of two variables, extension of 704
Function, positive definite, operator 711
Function, spectral 373 359
Function, support of 16 24
Functional, antilinear 9
Green's formula 75 221 502 560 588
Hilbert scale of spaces 240
Homeomorphism 2
Hyperbolic equations, perturbed, solution of 421 430
Identity, resolution of 13
Identity, resolution of, differentiation of 323
Identity, resolution of, generalized 13
Identity, resolution of, in separation of variables 463
Imbedding theorem 17
Inclusion operator 3
Inclusion, quasinuclear 48
Inclusion, topological 2
Integration by abstract measure 6
Interpolation theorem 240
interval 9
Involution 12
Kernel of the resolvent 187
Kernel, elementary positive definite 610
Kernel, generalized 47
Kernel, generalized spectral 337 347
kernel, hermitian 45 47
Kernel, positive definite 45 46 47
Kernel, spectral 337 352
Kernel, spectral integral 347
Kernel, theorem on 47—48 54—56 67
Krein — Milman theorem 537
Laplace expression in  416
Leibnitz formula 264
Local membership in a space 15 93 94
Matrix, Jacobi 503 591
Matrix, spectral 496 582 591
Measure 6
Measure, absolutely continuous 7
Measure, abstract, integration by 6
Measure, analytic 745
Measure, extreme spectral 516
Measure, finite 7
Measure, generalized 7
Measure, generalized, variation of 7
Measure, locally finite 7
| Measure, matrix 556
Measure, operator spectral 562
Measure, operator-valued 319 321
Measure, orthogonal spectral 514
Measure, product 8
Measure, spectral 336
Neighborhood, basic 1
Nevanlinna functions 534
Norms, positive and negative 31
Operator integrals 555
Operator, adjoint 9 11 35
Operator, averaging 26 610
Operator, Carleman 351
Operator, closed 10
Operator, closure of 10
Operator, closure of, by continuity 10
Operator, differential 79
Operator, differential, in an unbounded region 375
Operator, hermitian 11
Operator, Hilbert norm of 318
Operator, Hilbert — Schmidt 48 317
Operator, in pseudo-Hilbert space 557
Operator, inclusion 3
Operator, maximal 79
Operator, maximal, domain of definition for general differential expressions 273
Operator, maximal, for expressions with constant coefficients 273
Operator, maximal, for unbounded regions 376
Operator, maximal, strongly elliptic 182
Operator, minimal 79
Operator, minimal, domain of definition for general differential expressions 269
Operator, minimal, for expressions with constant coefficients 269
Operator, minimal, for unbounded regions 376
Operator, minimal, strongly elliptic 182
Operator, nonnegative 13
Operator, of generalized projection onto a generalized eigenmanifold 336
Operator, of orthogonal projection 11
Operator, of skew projection 11
Operator, on generalized vectors 35
Operator, positive 13
Operator, pseudo-linear 557
Operator, real 26 610
Operator, s-strong 90
Operator, s-weak 90
Operator, selfadjoint 11
Operator, strong 82 376
Operator, strong, for unbounded regions 376
Operator, trace of 52 318
Operator, weak 82 376
Operator, weak, for unbounded regions 376
Operator-valued measure 319 321
Operator-valued measure, differentiation of 319
Operator-valued measure, variation of 321
Parseval equality for difference operators 510 562 563 582 591
Parseval equality for general selfadjoint operators 323 325 335 337
Parseval equality for operators in  347 352 495
Polynomial of the first kind, induced by a difference expression 503 560
Polynomial of the second kind, induced by a difference expression 520 577 589
Polynomial, complete 277
Polynomial, relatively strong 383
Polynomial, relatively weak 383
Polynomial, subspace of linearity 277
Problem of moments, classical 724
Problem of moments, classical, determinate 725
Problem of moments, classical, indeterminate 725
Problem of moments, degenerate 729
Problem of moments, determinate 725
Problem of moments, determinate, many-dimensional 725
Problem of moments, finite 728
Problem of moments, indeterminate 725
Problem of moments, indeterminate, many-dimensional 725
Problem of moments, multidimensional degree 734
Problem of moments, Stieltjes 728
Pseudo-linear manifold 553
Pseudo-orthogonal sum 553
Pseudo-orthogonal supplement 553
Pseudo-orthonormal basis 550
Pseudo-scalar 548
Pseudo-scalar product 548
Pseudo-subspace 553
Pseudo-subspace, maximal 553
Pseudo-subspace, maximal, for unbounded regions 376
Pseudo-vectors 548
Quadratic forms, lower estimates of 104
Quasi-analytic classes of functions 726
Radon — Nikodym theorem 7
Resolution of the identity 13
Resolution of the identity, differentiation of 323
Resolution of the identity, for separation of variables 463
Resolution of the identity, generalized 13
Ring of sets 6
Schroedinger expression 386 420 431
Schroedinger expression, separation of variables 485
Separability, axiom of 3
Separation of variables for general operators 462
Separation of variables for general operators, in 478
Separation of variables for partial difference equations 605
Separation of variables for the Schroedinger expression 485
Set, Borel 8
Set, bounded 3
Set, bounded modulo subspaces 278
Set, closed 1
Set, closure of 1
Set, compact 4
Set, convex, extreme points of 516 537
Set, everywhere dense 1
Set, of full measure 7
Set, open 1
Set, precompact 4
Smoothness conditions, the usual 70
Smoothness of solutions of elliptic equations 161
Smoothness of solutions of elliptic equations, inside a region 164 168 172 174
Smoothness of solutions of elliptic equations, up to the boundary 178 253 257
Solution of elliptic equations, inside a region 164 168 172 174
Solution of elliptic equations, smoothness 161
Solution of elliptic equations, up to the boundary 178 253 257
Solution of perturbed hyperbolic equations 421 430
Solution, (r + s)-smooth 90
Solution, fundamental 161
Solution, fundamental system of 494 714
Solution, fundamental, in the classical sense 162
Solution, generalized, inside a region 95
Solution, generalized, up to the boundary 95
Solution, inside a region 95
Solution, r-smooth 83
Solution, s-generalized 90
Solution, semistrong 83
Solution, smooth 83
Solution, strong 83
Solution, up to the boundary 95
Solution, weak 83
Solution, weak, for the Cauchy problem 387
Solvability, conditional 69
Solvability, normal 87
Solvable Extension 80
Space with negative norm 32
Space with positive norm 32
Space, Banach 9
Space, complete 3
Space, equipment of 33 66
Space, Hausdorff 4
Space, Hilbert 10
Space, local membership in 15 93—94
Space, locally compact 4
Space, metric 3
Space, normal 4
Space, nuclear 67
Space, pseudo-Hilbert 548
Space, quasi-Hilbert 10
Space, regular 3
Space, separable 3
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