Linear Operators: Spectral theory |
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Page 1142
... present theorem in the range 1 < p ≤ 2 now follows at once from its validity in the range 2 ≤ p ≤∞ and from Lemma 9.14 . Q.E.D. In what follows , we will use the symbols p and to denote the η continuous extension to the classes C ...
... present theorem in the range 1 < p ≤ 2 now follows at once from its validity in the range 2 ≤ p ≤∞ and from Lemma 9.14 . Q.E.D. In what follows , we will use the symbols p and to denote the η continuous extension to the classes C ...
Page 1675
... present proof , Ê = d1F , so that d1 F is in H ( C ) . This completes the proof of the direct part of ( i ) of the present lemma . П To prove the converse , let F be in H ( C ) and let 1 be in H ( C ) . Let us agree to consider that ...
... present proof , Ê = d1F , so that d1 F is in H ( C ) . This completes the proof of the direct part of ( i ) of the present lemma . П To prove the converse , let F be in H ( C ) and let 1 be in H ( C ) . Let us agree to consider that ...
Page 1703
... present lemma . Q.E.D. 6. The Elliptic Boundary Value Problem Can the boundary value theory and the spectral theory of Chapter XIII be generalized to partial differential operators ? In the present section it will be seen that it can ...
... present lemma . Q.E.D. 6. The Elliptic Boundary Value Problem Can the boundary value theory and the spectral theory of Chapter XIII be generalized to partial differential operators ? In the present section it will be seen that it can ...
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