Linear Operators: Spectral theory |
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Page 1347
... evident advantage that it makes o , ( , λ ) an entire function of the complex variable 2 ; but it has drawbacks which , though less evident , are nevertheless decisive . - Suppose , for example , that we study the self adjoint operator ...
... evident advantage that it makes o , ( , λ ) an entire function of the complex variable 2 ; but it has drawbacks which , though less evident , are nevertheless decisive . - Suppose , for example , that we study the self adjoint operator ...
Page 1661
... evident , and instead of giving detailed statements which apply to our new context we shall simply refer to " Lemma 6 , " etc. , as " generalized to D1 ( I ) " when necessary . Lemma 10 applies similarly in an evident way to the new ...
... evident , and instead of giving detailed statements which apply to our new context we shall simply refer to " Lemma 6 , " etc. , as " generalized to D1 ( I ) " when necessary . Lemma 10 applies similarly in an evident way to the new ...
Page 1662
... evident consequence of Lemma 12 , as generalized to D1 ( I ) , which will be of importance to us in sub- sequent discussions , is stated in the following lemma . F 33 LEMMA . Let I be an open subset of the interior of C , and let F be ...
... evident consequence of Lemma 12 , as generalized to D1 ( I ) , which will be of importance to us in sub- sequent discussions , is stated in the following lemma . F 33 LEMMA . Let I be an open subset of the interior of C , and let F be ...
Contents
BAlgebras | 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 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