Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Davies E. — Spectral Theory and Differential Operators
Davies E. — Spectral Theory and Differential Operators

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Spectral Theory and Differential Operators

Автор: Davies E.

Аннотация:

This book is an introduction to the theory of partial differential operators. It assumes that the reader has a knowledge of introductory functional analysis, up to the spectral theorem for bounded linear operators on Banach spaces. However it describes the theory of Fourier transforms and distributions as far as is needed to analyse the spectrum of any constant coefficient partial differential operator. A completely new proof of the spectral theorem for unbounded self-adjoint operators is followed by its application to a variety of second order elliptic differential operators, from those with discrete spectrum to Schrodinger operators acting on L2(RN), The book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques.This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on the subject.


Язык: en

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 182

Добавлена в каталог: 09.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
Adams      67
Almost analytic      24
Banach algebras      22
Band, in spectrum      96
Bessel function      61 130
Biharmonic      113
boundary conditions      1
Cauchy’s Theorem      28
Cayley transform      11
Centre of mass      162
Coefficients, discontinuous      123
Coefficients, measurable      135
Coefficients, variable      118
Compact metric space      75
Convergence, norm resolvent      41
Convergence, strong      39
Convex region      117
Convolution      46
Coordinate neighbourhood      143
Cusp      146
Cyclic vector      34
Davies      ix 22
Deficiency index      12
Deficiency subspace      12
Degree      45
Dieudonne      vii
Diffeomorphism      142
Dinchlet boundary conditions      118 120
Dinchlet Laplacian      127
Dinchlet problem      ix 99
Dirac delta function      53
Distance function      107
distribution      53 121
Domain      2
Double well      171
Eigenfunction      2
Eigenfunction, boundary decay      136
Eigenspace      73
Eigenvalue      2
Eigenvalue, isolated      73
Eigenvalues, computation of      150
Eigenvalues, monotonicity of      136
Eigenvalues, of ball      130
Eigenvalues, of cube      127
Eigenvalues, of sector      131
Elastic membrane      99 118 140
Elastic plate      113
Electrostatic potential      99
Elliptic regularity theorem      133
Energy, ground state      155
Energy, kinetic      155
Energy, potential      155
Energy, total      155
Essential range      16
Essentially self-adjoint      8
Extension      2
Extension operator      145
Extension property      146
Finite element method      151
Fluid flow      140
Form closure      83
Form core      83
Form, closable      83
Form, closed      83
Form, quadratic      81
Form, semibounded      156
Form, sesquilinear      81
FOURIER      vii
Fourier transform      49
Fractional powers      79
Friedrichs      86
Friedrichs extension      86
Functional calculus      24
Gelfand      22
Gram — Schmidt      36
Graph      3
Green      11
Green function      94
Ground state      1SS
Haar measure      106
hadamard      64
Hamiltonian      188
Hardy      104
Hardy inequality      104
Harmonic function      134
Heat equation      99 118 140
Helfler      22
Helfler — Sjostrand formula      24
Helium atom      163
hilbert      vii
Hilbert — Schmidt operator      97
Hydrogen atom      163
Ideal of operators      97
interactions      161
Interpolation      63
Interval arithmetic      96
Isometric extension      11
Kato      19
Kufner      104
Laplace      11
Laplace — Beltrami operator      119
Laplacian      11
Lax      86
legendre      110
Legendre polynomial      10
Legendre’s equation      10 110
Liebnitz formula      26
Lipschitz boundary      146
Lipschitz condition      124
Locally $L^p$      156
Lower semicontinuous      82
Matrix, sparse      152
Matrix, tridiagonal      35
Milgram      86
Modifier      46
Monomial      48
Multi-index      45
Multi-index, degree of      45
Neumann boundary conditions      140
Neumann Laplacian      147
Neumann, von      22
Norm analytic      4
Operator, adjoint      7
Operator, biharmonic      113
Operator, closable      6
Operator, closed      3
Operator, closure      6
Operator, compact      66 75
Operator, conjugation      14
Operator, differential      57
Operator, divergence form      119
Operator, essentially self-adjoint      8
Operator, extension      2
Operator, finite rank      75
Operator, Hilbert — Schmidt      67
Operator, isometric      11
Operator, linear      2
Operator, local      71
Operator, multiplication      15
Operator, non-negative      78
Operator, real      14
Operator, resolvent      4
Operator, Schrodinger      155
Operator, self-adjoint      8
Operator, semibounded      78
Operator, singular elliptic      109
Operator, symmetric      6
Opic      104
Orthogonal complement      8
Partition of identity      144
periodic structure      96
Perturbation      17
Perturbation, compact      166
Perturbation, relatively bounded      17
Poincare      vii
Poisson problem      99
Polynomial      48
Potential      155
Potential, chemical      118
Potential, local singularities      159
Product of Banach spaces      3
Projection      40
Projection, spectral      41
Pseudodistance      107
Quantum theory      155 161
Rayleigh      88
Rayleigh — Ritz formula      88
Regular region      107
Relative bound      17
Rellich      19
Residue theorem      31
Resolvent equations      4
Riemann — Lebesgue lemma      49
Riemannian manifold      119
Riesz      75
Riesz representation theorem      37
Ritz — Galerkin method      100
Schrodinger      155
Schwartz      52
Schwartz space      45
Self-adjoint      8
Semigroup      101
Separable      8
Simon      156
Singular elliptic      109
Sjostrand      22
Smooth      11 45
Sobolev      52
Sobolev space      67 124
Spectral theorem      32
Spectrum      4
Spectrum, discrete      73
Spectrum, essential      73 167
Spectrum, negative      168
Spectrum, point      73
Spectrum, positive      164
Spin      155
Square root      80
Statistics      155
Stokes’ formula      26
Stone      22
Stone — Weierstrass theorem      32
Sturm — Liouville operator      94
Subspace, cyclic      34
Subspace, invariant      33
Subspace, spectral      41
Symbol      58
Symbol, principal      59
Taylor’s Theorem      30
Tempie — Lehmann formula      95
Three lines lemma      64
Threshold      169
Translation invariance      57
Triangulation of region      151
Turbine blade      113
Uniform ellipticity      60
Unitary equivalence      36
Unitary group      44
Variational formulae      88
Vertex of region      131
Weak derivative      54 121
Zorn’s Lemma      35
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте