Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 73
Page 1120
... assume for simplicity of statement that Hilbert space is separable . Subdiagonal representations of an operator are connected with the study of its invariant subspaces . Thus , the key to the situation that we wish to analyze is the ...
... assume for simplicity of statement that Hilbert space is separable . Subdiagonal representations of an operator are connected with the study of its invariant subspaces . Thus , the key to the situation that we wish to analyze is the ...
Page 1629
... assumed to be defined for t = [ t , . . . , t1 ] in D , to be symmetric in the indices i1 , i , . . . , i ,, and ... assume for 1629 Linear Partial Differential Equations and Operators 1 Introduction The Cauchy Problem, Local Dependence.
... assumed to be defined for t = [ t , . . . , t1 ] in D , to be symmetric in the indices i1 , i , . . . , i ,, and ... assume for 1629 Linear Partial Differential Equations and Operators 1 Introduction The Cauchy Problem, Local Dependence.
Page 1717
... assume assume without loss of generality that d ̧ ‚ ‚ ( x ) = d ̧‚Ï ( x ) for x in I。, | J1 | = | J2 | = p . Thus , if we put Το = Σ │J2 | = | J2 = p To is formally symmetric ; To = * . We XIV.6.10 THE ELLIPTIC BOUNDARY VALUE PROBLEM ...
... assume assume without loss of generality that d ̧ ‚ ‚ ( x ) = d ̧‚Ï ( x ) for x in I。, | J1 | = | J2 | = p . Thus , if we put Το = Σ │J2 | = | J2 = p To is formally symmetric ; To = * . We XIV.6.10 THE ELLIPTIC BOUNDARY VALUE PROBLEM ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Copyright | |
59 other sections not shown
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T unique unitary vanishes vector zero