Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1000
... uniformly on each compact subset on the half - plane ( 2 ) > 0. If { f } were known to be uniformly convergent in a neighborhood of U , the analyticity of its limit f , would be clear . Unfortunately it is not clear that the sequence f ...
... uniformly on each compact subset on the half - plane ( 2 ) > 0. If { f } were known to be uniformly convergent in a neighborhood of U , the analyticity of its limit f , would be clear . Unfortunately it is not clear that the sequence f ...
Page 1001
... uniformly on any portion of Q whose closure contains neither a nor b . Let M be a bound for the sequence yn so that ... uniformly on Q to the function g given by the equations g ( z ) = fy ( z ) ( z — a ) 2 ( z — b ) 2 , = 0 za , b , z ...
... uniformly on any portion of Q whose closure contains neither a nor b . Let M be a bound for the sequence yn so that ... uniformly on Q to the function g given by the equations g ( z ) = fy ( z ) ( z — a ) 2 ( z — b ) 2 , = 0 za , b , z ...
Page 1108
... uniformly in i , ( ii ) lim , it follows that - > i Σ , 2 , ( m ) = 0 uniformly in m , i = r ( iii ) Σ12 , ( m ) | * is bounded uniformly in m , ( iv ) i∞ ( m ) → 0 as i co uniformly in m . Thus , by the above inequality , ∞ ( −1 ) ...
... uniformly in i , ( ii ) lim , it follows that - > i Σ , 2 , ( m ) = 0 uniformly in m , i = r ( iii ) Σ12 , ( m ) | * is bounded uniformly in m , ( iv ) i∞ ( m ) → 0 as i co uniformly in m . Thus , by the above inequality , ∞ ( −1 ) ...
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