Linear Operators: Spectral theory |
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Page 1011
... S || for every S and T in HS . PROOF . It is evident that if T is in HS and a is a scalar , then || aT || = | a ... Tm → 0 . It follows from Lemma 2 that T - Tm → 0 and so there is a bounded linear operator T in § with | T - Tn│ → 0 ...
... S || for every S and T in HS . PROOF . It is evident that if T is in HS and a is a scalar , then || aT || = | a ... Tm → 0 . It follows from Lemma 2 that T - Tm → 0 and so there is a bounded linear operator T in § with | T - Tn│ → 0 ...
Page 1761
... s ) d2 , + b ( x ; 8 ) , ( 12 ) so that = ρ Əs - Po · Let η j = 1 100 be a ... TM ( ( Рo − 2 ) m + 1ƒ ) ( x ) , = These last expressions make it plain ... s . Hence , by ( viii ) , there exists a function h in ĈK ́ ̄ ' ( C1 ) , all of ...
... s ) d2 , + b ( x ; 8 ) , ( 12 ) so that = ρ Əs - Po · Let η j = 1 100 be a ... TM ( ( Рo − 2 ) m + 1ƒ ) ( x ) , = These last expressions make it plain ... s . Hence , by ( viii ) , there exists a function h in ĈK ́ ̄ ' ( C1 ) , all of ...
Page 2
... S every sequence yn → yo there is a sequence xn Nyn and Tan = Yn ' n = 0 , 1 , .... page 72 , line 10 : page 72 ... TM ( S ) into itself , and substitute : the space of totally measurable scalar functions into itself . page 106 , line ...
... S every sequence yn → yo there is a sequence xn Nyn and Tan = Yn ' n = 0 , 1 , .... page 72 , line 10 : page 72 ... TM ( S ) into itself , and substitute : the space of totally measurable scalar functions into itself . page 106 , line ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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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 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 prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero