Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 955
... linear functional h , and since , by IX.2.3 , every such function is continuous , it follows that a multiplicative linear functional on A is entirely determined by its restriction to A. Thus , there is a unique point P∞ in M such that ...
... linear functional h , and since , by IX.2.3 , every such function is continuous , it follows that a multiplicative linear functional on A is entirely determined by its restriction to A. Thus , there is a unique point P∞ in M such that ...
Page 1293
... function g in H ( I ) such that t * g and the assertion reduces to [ * f ( t ) x * g ( t ) dt = 0 which is the hypothesis of the theorem . = w , ( E ) Suppose now that some linear functional y on L2 ( I ) , represented by a function h ...
... function g in H ( I ) such that t * g and the assertion reduces to [ * f ( t ) x * g ( t ) dt = 0 which is the hypothesis of the theorem . = w , ( E ) Suppose now that some linear functional y on L2 ( I ) , represented by a function h ...
Page 1797
... linear functionals . Proc . Amer . Math . Soc . 4 , 375–387 ( 1953 ) . Cameron , R. H. , Lindgren , B. W. , and Martin , W. T. 1 . Linearization of certain non - linear functional equations . Proc . Amer . Math . Soc . 3 , 138-143 ...
... linear functionals . Proc . Amer . Math . Soc . 4 , 375–387 ( 1953 ) . Cameron , R. H. , Lindgren , B. W. , and Martin , W. T. 1 . Linearization of certain non - linear functional equations . Proc . Amer . Math . Soc . 3 , 138-143 ...
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