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 ( T1 ) , then f1g and fag are also in D ( T1 ) . Since the map g → fig 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 ...
... clear that if g is in D ( T1 ) , then f1g and fag are also in D ( T1 ) . Since the map g → fig 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 ...
Page 1652
... clear that { F } converges to some F in L2 ( I ) . Similarly , since | F ( x ) ≥│F2 for each F in H ( * ) ( I ) and each index J such that Jk , it is clear that if Jk , the sequence { F } converges to some F , in L2 ( I ) . Let q be ...
... clear that { F } converges to some F in L2 ( I ) . Similarly , since | F ( x ) ≥│F2 for each F in H ( * ) ( I ) and each index J such that Jk , it is clear that if Jk , the sequence { F } converges to some F , in L2 ( I ) . Let q be ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum 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(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero