Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
From inside the book
Results 1-3 of 70
Page 1559
... Suppose that the function Q is positive , continuous , of bounded variation on every finite interval , non - increasing , and that ∞ √ Q ( s ) -1ds = ∞ . Suppose that N ( t ) satisfies the condition of the preceding exercise . Prove ...
... Suppose that the function Q is positive , continuous , of bounded variation on every finite interval , non - increasing , and that ∞ √ Q ( s ) -1ds = ∞ . Suppose that N ( t ) satisfies the condition of the preceding exercise . Prove ...
Page 1597
... suppose that lim q ( t ) t → b = C. Then the essential spectrum of 7 is the semi - axis [ c , ∞ ) ( 7.16 ) . ( 20 ) In the interval [ 0 , ∞ ) , suppose that the function q ( t ) —c is of class L , [ 0 , ∞ ) for some p , 1 ≤ p ...
... suppose that lim q ( t ) t → b = C. Then the essential spectrum of 7 is the semi - axis [ c , ∞ ) ( 7.16 ) . ( 20 ) In the interval [ 0 , ∞ ) , suppose that the function q ( t ) —c is of class L , [ 0 , ∞ ) for some p , 1 ≤ p ...
Page 1602
... suppose that the equation ( 2-7 ) f linearly independent solutions ƒ and g such that = O has two S ' ' \ f ' ( s ) | 2 ds = O ( 12 ) and [ ' * ' \ g ' ( s ) \ 2 ds = O ( t2 ) . Then the point belongs to the essential spectrum of 7 ...
... suppose that the equation ( 2-7 ) f linearly independent solutions ƒ and g such that = O has two S ' ' \ f ' ( s ) | 2 ds = O ( 12 ) and [ ' * ' \ g ' ( s ) \ 2 ds = O ( t2 ) . Then the point belongs to the essential spectrum of 7 ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
57 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 Haar measure 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 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 transform unique unitary vanishes vector zero