Grubb G. — Functional Calculus of Pseudo-Differential Boundary Problems :: Электронная библиотека попечительского совета мехмата МГУ

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Grubb G. — Functional Calculus of Pseudo-Differential Boundary Problems

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Название: Functional Calculus of Pseudo-Differential Boundary Problems

Автор: Grubb G.

Аннотация:

The theory of pseudo-differential operators has been developed as a powerful tool to handle particial differential equqtions. Here the pseudo-differential operators, and more generally the Fourie integral operators, include as special cases both the differential operators, their solution operators (integral operators), and compositions of these types. For equations on manifolds with boundary, Eskin, Vishik and Boutet de Monvel invented in particular the calculus of pseudo-differential boundary operators, that applies to elliptic boundary value problems.
The aim of this book is to develop a functional calculus for such operators; i.e. to find the structure and properties of functions of these operators defined abstractly by functional analysis.

Язык:

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1986

Количество страниц: 518

Добавлена в каталог: 05.11.2004

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Предметный указатель

Adjoint of Poisson operator      (1.2.34) 2.4.1
Adjoint of ps.d.o.      1.2.1 2.1.15
Adjoint of realization      1.6.9
Adjoint of singular Green operator      (1.2.47) 2.4.1
Adjoint of trace operator      (1.2.34) 2.4.1
Agmon condition      1.6
Analytic dependence on parameters      3.1.7 3.2.6 3.2.9 3.3 3.3.9
Anisotropic Sobolev spaces      (A.23—24) ff.
Auxiliary elliptic operators      (3.1.14) 3.1.2 (3.1.18) 3.1.5 3.2.15
Ball      (A.3)
Biharmonic operator      (1.5.13) 4.4.1 4.7.2
Boundary realization      (1.4.11')
Boundary symbol operator      (1.2.25 (2.4.2—6) (3.1.1—4)
Cauchy trace operator      (A.55)
Characteristic values      (A.72)
Co-Fourier transform      (A.13)
Coercive      1.7 (1.7.4)
Complex powers of quadratic systems      (3.4.14) ff. 3.4.3 (4.4.46)
Complex powers of realizations      3.4.5 4.4
Complex powers of zero-order operators      3.4.4
Composition of -dependent symbols      2.7
Composition of -independent symbols      2.6
Composition of $\mu$ -dependent operators      2.7
Composition of boundary symbol operators      2.6
Composition of Green operators      (1.2.52) 2.6 2.7
Composition of operators on manifolds      2.7
Composition of ps.d.o.s      1.2.1 2.1.15 (2.6.16—23) 2.7.7
Composition of realizations      1.4.6
Conormal bundle      2.4.12
Conormal distribution      2.4.12
Continuity of Poisson operators      (1.2.23) 2.5.1
Continuity of ps.d.o.s      1.2.1 (1.2.8) 2.1.12 2.5.5
Continuity of singular Green operators      (1.2.46) 2.5.4
Continuity of trace operators      (1.2.27) 2.5.2 2.5.3
Continuous extension operators      (A.34) (A.39)
Coordinate change      2.1.17 2.2.12 2.4.10—12
Cotangent bundle      (A.62) ff.
Counting function      (A.80—82) 4.5
Deviation operators      (4.7.42—52) ff. 4.7.12
Diagonal -integral of complex power kernel      4.4.7
Diagonal -integral of heat kernel      (4.2.106) ff.
Diagonal -integral of resolvent kernel      (3.3.65)
Dilation      2.4.13
Dirichlet problem      (1.6.56) (1.6.66) 1.7.2 4.4.1 4.7
Dirichlet trace operator      (1.C.56) ff.
Dirichlet-type problem      1.5.11 (1.5.58) 1.6.12 1
Distributions      (A.9') ff.
Douglis — Nirenberg system      (4.6.27) ff. 4.6.3 4.6.4
Dual spaces      (A.22) ff. (A.39)
Eigenvalue estimates      Section A.6 4.5
Elliptic Green operator (symbol)      (1.2.53) ff. 3.1.3 3.1.4
Elliptic ps.d.o. (symbol)      (1.2.53) ff. 1.5.2 2.1.2 2.1.11 2.1.16 2.8.1
Elliptic realization      1.4.1 1.7.8
Essential spectrum      (A.94) ff. (3.4.23)
Evolution problem      (1.1.5) 4.1
Extended singular Green operator      (3.2.16—22)
Extension by zero      (A.31) (A.64)
First symbol seminorms      (2.3.13) 2.3.7
Formal adjoint      (1.6.24) 1.6.9
Fourier transform      (A.13)
Fractional powers      3.4.5 4.4.1 (4.4.10') 4.4.2 4.5.11
Fredholm property      (A.94) ff. 3.1.1
Friedrichs extension      1.7.2 ff.
Functions of zero-order operator      3.4.4
Garding inequality      (1.7.2) 1.7
Generalized singular Green operator      4.4.1 ff. 4.4.4 4.5.8
Green operator      (1.2.14) (2.4.10)
Green's formula      1.3.2 1.6.1 1.6.2 (2.2.38—39)
Green's matrix      1.3.2 (1.3.1
Hankel operator      2.6.12 3.1.1
Heat equation      1.5.1 4.1 4.2
Heat operator      4.1 4.2
Heat operator trace      4.2.7 (4.2.68) 4.2.11 4.2.12
Hilbert — Schmidt operator      (A.77) ff. 3.1.1 (3.2.3)
Hoelder property      2.1.10 2.1.10' 2.1.11 2.8.3
Hoelder space      (A.8) ff. 2.1.10' 4.1.1
Holomorphic extension      2.2.3
Implicit eigenvalue problem      4.6 4.6.1—4
Improved regularity      2.6.11 3.2.5 3.2.8 3.2.11 (3.3.75)
Inclusions between Sobolev spaces      (A.27—28) (A.44)
INDEX      (A.94) 1.7.3 (3.1.9) (3.1.42) 4.3
Index bundle      3.1.6
Index formula      4.3 (4.3.13)
Interpolation      (A.47) ff. 2.2.10 (2.6.42) 4.4.2—3
Interpolation inequality      (A.49)
Interpolation of Sobolev spaces      (A.46)
Invariance      (A.56) ff. A.3 2.1.17 2.2.12 2.4.10—12
Isotropic Sobolev spaces      (A.26) (A.29)
Iterated boundary problem      (3.4.6)
J, reflection      (A.32)
Kernel      (1.2.4) 2.4
Keyhole region      (3.1.46) (4.2.1)
Laguerre expansions      2.2 (2.2.49) (2.2.54) (2.3.30)
Laguerre functions      (2.2.10—11)
Laguerre operator      (2.2.12) (2.2.13) (4.5.28)
Laplace operator      1.1.1 1.5.11—13 1.6.13—16 1.7.6 1.7.15—17 4.7
Laurent loop      (4.4.4)
Leibniz' formula      (A.7)
Local Sobolev spaces      (A.29) ff. (A.45) (A.68)
m-bounded      (1.7.66) 1.7.11 1.7.13
m-coercive      (1.7.4) 1.7.8 (1.7.91) (1.7.98) 1.7.15—17
Manifold Section      A.5
Maximal realization      (1.4.1)
Maximum-minimum principle      Section A.6 4.5.1 4.5.3
Minimal realization      (1.4.1—2)
Minimum-maximum property      (A.75) ff.
Negative part of number      (A.4')
Negative part of operator      (A.73) ff. (4.5.60)
Negative regularity      1.5.13 2.1.19 3.2.16 4.7
Negligible      (2.1.37—40) 2.3.11 2.4.3
Neumann trace operator      (1.6.56) ff.
Neumann-type problem      1.5.12 (1.5.59) 1.6.14 1.7.16

Non-characteristic      (1.3.14) ff. 1.3.4
Non-integer norms      2.2.10 (2.6.42) 3.3.10
Normal boundary condition      1.4.3
Normal boundary value problem      1.4.3 1.5.7
Normal coordinate      (A.61) ff. 2.4.12
Normal realization      1.4.3
Normal trace operator      1.4.3
Order reducing operators      (1.2.52') 3.1.2 (3.1.48) 3.2.15
Parabolic      1.5.3 1.5.5
Parameter-dependent Sobolev spaces      Sections A.4—5 2.5 (4.7.3)
Parameter-dependent symbol-kernels      (2.3.25) ff.
Parameter-dependent symbols      2.1.1 2.3.2—3 2.3.7—8
Parameter-elliptic Green operator      1.5.5 3.1.3 3.3
Parameter-elliptic Green symbol      1.5.5 3.1.3 3.3
Parameter-elliptic ps.d.o.      1.5.3 2.1.2
Parameter-independent calculus      Chapter 1 2.3.13 4.3—5
Parameter-independent symbol norm      (4.5.27)
Parameter-independent symbols      1.2 2.3.13
Parametrix      (1.2.54) 1.4.2 2.1.16 3.2.3 3.3.1
Parseval — Plancherel theorem      (A.15)
Partial Fourier transform      (A.18)
Perturbation lemmas      A.5 A.6 A.7
Perturbation of spectral      Section A.6 4.5
Perturbed solution expansion      4.7.11
Perturbed solution operator      4.7.8 4.7.13
Plus-integral      (2.2.42) ff.
Poisson operator      (1.2.29) (2.4.8)
Poisson symbol      (1.2.30) 2.3.3
Poisson symbol-kernel      (1.2.29) ff. (2.3.25)
Poles of complex power trace      4.4.7 4.4.8
Polyhomogeneous      (1.2.3) 2.1.1 2.3.3 2.3.8
Polynomially parameter-dependent      3.4 3.4.1
Positive part of number      (A.4')
Positive part of operator      (A.73) ff. (4.5.60)
Powers of the resolvent      3.4.2
Principal boundary symbol operator      (3.1.1) (3.1.4)
Principal symbol (part)      (1.2.3) ff. (1.2.24) 2.1.1 2.3.2
Projections in symbol spaces      2.2.2 2.3.9—10 2.6.2—3
Proper      1.2.1
ps.d.o.      see pseudo-differential operator
Pseudo-differential operator      (1.2.1) (2.1.29)
Pseudo-differential symbol      (1.2.2) 2.1.1
Quasi-homogeneous      (1.2.22) (1.2.40) (2.3.27) (2.3.29)
Quasi-norm      (A.78) (4.5.15)
Quotient spaces      (A.36) ff.
Realization      1.4.1
Reconstruction principle      (2.1.7) ff. 2.3.8'
Reflection operator J      (A.32) (1.2.51)
Regularity number      (1.5.6) ff. 1.5.14 2.1.1 2.3.3 2.3.8
Regularizable problems      4.7
Remainder estimates      4.5.4—7 4.5.12—13
Resolvent of Green operator      3.4 3.4.3
Resolvent of quadratic system      3.4 3.4.3
Resolvent of realization      (1.5.18) ff. 3.3
Restriction      (A.30) (A.58) (A.64)
s.g.o.      see singular Green operator
s.g.o. symbol seminorm      2.3.7 ff. (4.5.27)
Schatten class      (A.77)
Schwartz space      (A.9") ff.
Seeley extension      (1.2.48) ff. 2.4.12
Selfadjoint realization      1.6.11 4.4.2 4.5 4.6
Sesquilinear duality      (A.11—12) (A.22)
Singular Green operator      (1.2.36—37) (2.4.8)
Singular Green symbol      (1.2.41 2.3.8
Singular Green symbol-kernel      (1.2.43) (2.3.25)
Singular perturbation      1.5.13 4.7
Singularly perturbed Dirichlet problem      4.7.2 4.7.9—10 4.7.14—16
Smooth bounded open set      A.3
Sobolev estimates      2.1.12 2.5 4.7
Sobolev norms Sections      A.3—5 (4.7.3)
Sobolev spaces Sections      A.3—5
Spectral coefficient      (4.5.1—5)
Spectral estimates      4.5 4.6
Spectral estimates for generalized s.g.o.s      4.5.2 4.5.8—10 (4.5.51—52)
Spectral estimates for ps.d.o.s      4.5.3 4.5.5 4.5.12 (4.5.58)
Spectral estimates for realizations      4.5.1 4.5.4 4.5.6 4.5.11—14
Spectral estimates two-sided      4.5.4 4.5.13 4.5.14 4.6
Spectrum      Section A.6 4.5
Square root      3.4.5 4.4 4.4.1
Standard trace operators      (A.50) A.2 (A.55) (A.67)
Strictly homogeneous      2.1.8 2.8
Strictly homogeneous boundary symbol operator      (3.1.2)
Strictly homogeneous symbols      2.1.8—9 2.8
Strongly elliptic      (1.7.1)
Symbol seminorms      2.1.3 ff. (2.3.12') 2.3.7
Symbol spaces for Poisson operators      2.3.2 2.3.3 2.3.13
Symbol spaces for ps.d.o.s      (1.2.2) ff. 2.1.1
Symbol spaces for singular Green operators      2.3.7 2.3.8 2.3.13
Symbol spaces for trace operators      2.3.2 2.3.3 2.3.13
Symbol-kernel of Poisson operator      (1.2:29) (2.3.25) 2.3.13
Symbol-kernel of singular Green operator      (1.2.43) (2.3.25) 2.3.13
Symbol-kernel of trace operator      (1.2.23) (2.3.25) 2.3.13
Taylor's formula      (A.6)
Toeplitz operator      2.2.11
Trace class operator      (A.77) ff.
Trace of complex power      4.4.8
Trace of heat operator      (4.2.64
Trace of resolvent      (3.3.33) (3.3.67) (3.3.74')
Trace operator      (1.2.17—18) (2.4.8)
Trace symbol      (1.2.23') 2.3.3
Trace symbol-kernel      (1.2.23) (2.3.25)
Transmission property      (1.2.7—12) 2.2.4 2.2.7 2.2.12
Truncated sector      (3.1.47) (4.1.3)
Uniformly negligible      2.4.4 2.4.8
V-coercive      (1.7.6)
Variational operator      1.7.1 ff. 1.7.2 1.7.9
Vector bundle      (A.62) ff.
Weak semibgundedness      1.7.4 1.7.11
Weighted -space      (A.21) ff.
Weyl — Ky Fan theorem      A.6
Wiener — Hopf calculus      2.2
x-form, y-form, -form, etc.      (2.1.29) ff. 2.1.15 2.4.6 2.4.9

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