Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1000
... clear . Unfortunately it is not clear that the sequence f is uniformly con- vergent on any region containing an interval of the real axis and so an additional argument is needed . Let U be the open interval ( a , b ) and Q the rectangle ...
... clear . Unfortunately it is not clear that the sequence f is uniformly con- vergent on any region containing an interval of the real axis and so an additional argument is needed . Let U be the open interval ( a , b ) and Q the rectangle ...
Page 1298
... clear that if g is in D ( T ) , then fig and fag are also in D ( T1 ) . Since the map f1g of D ( T1 ) into itself is clearly closed , it is , by the closed graph theorem ( II.2.4 ) , continuous . Let B be a boundary value for τ and ...
... clear that if g is in D ( T ) , then fig and fag are also in D ( T1 ) . Since the map f1g of D ( T1 ) into itself is clearly closed , it is , by the closed graph theorem ( II.2.4 ) , continuous . Let B be a boundary value for τ and ...
Page 1652
... clear that { F } converges to some F in L ( I ) . Similarly , since | FF , for each F in H ( * ) ( I ) and each index J such that J≤k , it is clear that if | J | ≤k , the sequence { F } converges to some F , in La ( I ) . Let q be in ...
... clear that { F } converges to some F in L ( I ) . Similarly , since | FF , for each F in H ( * ) ( I ) and each index J such that J≤k , it is clear that if | J | ≤k , the sequence { F } converges to some F , in La ( I ) . Let q be in ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero