Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 38
Page 1563
... essential spectrum of 7 contains the positive semi - axis . ( Hint : Apply Theorem 7.1 . ) G41 Suppose that the function q is bounded below . Suppose that the origin belongs to the essential spectrum of 7 . ( a ) Let { f } be a sequence ...
... essential spectrum of 7 contains the positive semi - axis . ( Hint : Apply Theorem 7.1 . ) G41 Suppose that the function q is bounded below . Suppose that the origin belongs to the essential spectrum of 7 . ( a ) Let { f } be a sequence ...
Page 1600
Nelson Dunford, Jacob T. Schwartz. meets the essential spectrum of 7 ( Hartman and Putnam [ 2 ] ) . ( 36 ) Suppose the function q is twice differentiable , and let ( 2 , μ ) be an open interval which does not meet the essential spectrum ...
Nelson Dunford, Jacob T. Schwartz. meets the essential spectrum of 7 ( Hartman and Putnam [ 2 ] ) . ( 36 ) Suppose the function q is twice differentiable , and let ( 2 , μ ) be an open interval which does not meet the essential spectrum ...
Page 1601
... essential spectrum of contains the positive semi - axis ( Šnol [ 1 ] , Exercise 9.G 40 ) . The following are criteria for deciding whether a particular point λ lies in the essential spectrum of t . ( 42 ) On the interval [ 0 , ∞ ) , if ...
... essential spectrum of contains the positive semi - axis ( Šnol [ 1 ] , Exercise 9.G 40 ) . The following are criteria for deciding whether a particular point λ lies in the essential spectrum of t . ( 42 ) On the interval [ 0 , ∞ ) , if ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
45 other sections not shown
Other editions - View all
Common terms and phrases
A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero