Linear Operators: Spectral theory |
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Page 1087
... suppose in addition that the number 2 is in I and that T2 is Hermitian . Show that o ( T2 ) Co ( T , ) for every p in I. 2 54 Let the hypotheses of Exercise 50 be satisfied , and suppose in addition that ( S , E , μ ) is finite . Let p ...
... suppose in addition that the number 2 is in I and that T2 is Hermitian . Show that o ( T2 ) Co ( T , ) for every p in I. 2 54 Let the hypotheses of Exercise 50 be satisfied , and suppose in addition that ( S , E , μ ) is finite . Let p ...
Page 1563
... 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 in D ( T。( t ) ) such that | fn | Tf0 , and such that f , vanishes in the interval [ 0. n ) ...
... 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 in D ( T。( t ) ) such that | fn | Tf0 , and such that f , vanishes in the interval [ 0. n ) ...
Page 1602
... suppose that the equation ( 2-7 ) = 0 has two linearly independent solutions ƒ and g such that S ' ' \ f ' ( s ) \ 2 ds = O ( t2 ) and t [ ' * ' \ g ' ( s ) \ 2 ds = O ( t2 ) . Then the point λ belongs to the essential spectrum of 7 ...
... suppose that the equation ( 2-7 ) = 0 has two linearly independent solutions ƒ and g such that S ' ' \ f ' ( s ) \ 2 ds = O ( t2 ) and t [ ' * ' \ g ' ( s ) \ 2 ds = O ( t2 ) . Then the point λ belongs to the essential spectrum of 7 ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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