Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 ʼn to denote the 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 ʼn to denote the continuous extension to the classes C ...
Page 1675
... present proof , F = d1F , so that 1 F is in H ( C ) . This completes the proof of the direct part of ( i ) of the present lemma . π To prove the converse , let F be in H ( C ) and let a1 be in H ( C ) . Let us agree to consider that ...
... present proof , F = d1F , so that 1 F is in H ( C ) . This completes the proof of the direct part of ( i ) of the present lemma . π To prove the converse , let F be in H ( C ) and let a1 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 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula 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 linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero