Linear Operators, Part 2 |
From inside the book
Results 1-3 of 68
Page 1279
... interval of the real axis . The interval I can be open , half - open , or closed . The interval [ a , co ) is considered to be half - open ; the interval ( -∞ , ∞ ) to be open . Thus a closed interval is a compact set . An end point t ...
... interval of the real axis . The interval I can be open , half - open , or closed . The interval [ a , co ) is considered to be half - open ; the interval ( -∞ , ∞ ) to be open . Thus a closed interval is a compact set . An end point t ...
Page 1539
... interval [ 0 , ∞ ) . Prove that a complex number 2 belongs to the essential spectrum of 7 if and only if there exists a sequence { f } of functions in D ( To ( T ) ) such that f2 = 1 , f , vanishes in the interval [ 0 , n ] , and as n ...
... interval [ 0 , ∞ ) . Prove that a complex number 2 belongs to the essential spectrum of 7 if and only if there exists a sequence { f } of functions in D ( To ( T ) ) such that f2 = 1 , f , vanishes in the interval [ 0 , n ] , and as n ...
Page 1599
... interval [ 0 , ∞ ) . Then on the positive real axis every interval of length K contains a point of the essential spectrum of 7 ( Glazman [ 4 ] , Exercise 9.A 6 ) . ( 32 ) On the interval [ 0 , ∞ ) , if q ( t ) tends monotonically to ...
... interval [ 0 , ∞ ) . Then on the positive real axis every interval of length K contains a point of the essential spectrum of 7 ( Glazman [ 4 ] , Exercise 9.A 6 ) . ( 32 ) On the interval [ 0 , ∞ ) , if q ( t ) tends monotonically to ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
36 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 domain 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 linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero