Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
From inside the book
Results 1-3 of 7
Page 2000
... sphere in RN . Then , by changing to spherical polar coordinates ( r , w ) where s = rw with r≥ 0 , w = 1 , we have , for 0 < ε < r , √esiuis , If ( 8 ) | ds = st = [ [ { { _ \ / ( pu ) p = { m ( dev ) dp = ε M • T dp ερ { √ \ f ( w ) ...
... sphere in RN . Then , by changing to spherical polar coordinates ( r , w ) where s = rw with r≥ 0 , w = 1 , we have , for 0 < ε < r , √esiuis , If ( 8 ) | ds = st = [ [ { { _ \ / ( pu ) p = { m ( dev ) dp = ε M • T dp ερ { √ \ f ( w ) ...
Page 2309
... sphere of L2 ( 1 ) , and { f } a sequence of elements of S - 1U , then f , may be written as fn = S - 1gn with gn in U. The space L2 ( I ) being reflexive , the sequence { g } has a weakly convergent subse- quence with weak limit g ...
... sphere of L2 ( 1 ) , and { f } a sequence of elements of S - 1U , then f , may be written as fn = S - 1gn with gn in U. The space L2 ( I ) being reflexive , the sequence { g } has a weakly convergent subse- quence with weak limit g ...
Page 2438
... sphere Σ in Е " , so that [ __ f ( x ) dx = [ ® " { { f ( rw ) r " = 1 } μ ( dw ) dr ΕΠ for each Borel measurable function ƒ defined on En which is either integrable over En or non - negative . If ƒ is a Borel measurable function on E ...
... sphere Σ in Е " , so that [ __ f ( x ) dx = [ ® " { { f ( rw ) r " = 1 } μ ( dw ) dr ΕΠ for each Borel measurable function ƒ defined on En which is either integrable over En or non - negative . If ƒ is a Borel measurable function on E ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
23 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero