Linear Operators: Spectral theory |
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Page 945
... fact , the theory will be applied in this section to prove the principal result in H. Bohr's theory of almost periodic functions . It has been observed ( IV.7.6 ) that there is a compact Hausdorff space S such that AP is isometrically ...
... fact , the theory will be applied in this section to prove the principal result in H. Bohr's theory of almost periodic functions . It has been observed ( IV.7.6 ) that there is a compact Hausdorff space S such that AP is isometrically ...
Page 1245
... fact that each complex number x has a unique representation a = α reio where r≥ 0 , and e1o | 1. By analogy with the fact that r we shall first seek to obtain the self adjoint operator A from the operator T * T . = = 1 LEMMA . Let T be ...
... fact that each complex number x has a unique representation a = α reio where r≥ 0 , and e1o | 1. By analogy with the fact that r we shall first seek to obtain the self adjoint operator A from the operator T * T . = = 1 LEMMA . Let T be ...
Page 1348
... fact makes evident what could readily be suspected before : that from the point of view of the negative real axis , a more favorable choice of basis for the solutions of to λσ is ô1 ( t , λ ) = ô1⁄2 ( t , λ ) = et√Fλ Το = τσ = Of ...
... fact makes evident what could readily be suspected before : that from the point of view of the negative real axis , a more favorable choice of basis for the solutions of to λσ is ô1 ( t , λ ) = ô1⁄2 ( t , λ ) = et√Fλ Το = τσ = Of ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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 complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero