Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 78
Page 1454
... equal . PROOF . To prove ( a ) , note that if T is bounded below , there exists a constant K such that ( Tx , x ) ≥ −K ( x , x ) , x = D ( T ) . The proof of Theorem 5 now shows that σ , ( T ) is a subset of the half- axis oot -K ...
... equal . PROOF . To prove ( a ) , note that if T is bounded below , there exists a constant K such that ( Tx , x ) ≥ −K ( x , x ) , x = D ( T ) . The proof of Theorem 5 now shows that σ , ( T ) is a subset of the half- axis oot -K ...
Page 1539
... equal deficiency indices , and let λ be a real number . Prove that the distance from 2 to the essential spectrum of t is less than or equal to K if and only if there exists a sequence ƒ „ in D ( To ( T ) ) such that f = 1 , f vanishes ...
... equal deficiency indices , and let λ be a real number . Prove that the distance from 2 to the essential spectrum of t is less than or equal to K if and only if there exists a sequence ƒ „ in D ( To ( T ) ) such that f = 1 , f vanishes ...
Page 1735
... equal to 1 in a neighborhood of p = 0 and identically equal to zero outside the unit sphere in E " . Let § in Co ( E " ) be identically equal to 1 in a neighborhood of the unit closed sphere in E and identically zero outside the sphere ...
... equal to 1 in a neighborhood of p = 0 and identically equal to zero outside the unit sphere in E " . Let § in Co ( E " ) be identically equal to 1 in a neighborhood of the unit closed sphere in E and identically zero outside the sphere ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
52 other sections not shown
Other editions - View all
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(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 satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero