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 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 ...
Page 1756
... present theorem is shown to be a consequence of ( ii ) . The remainder of the present proof is devoted to showing that ( ii ) is valid for each fixed r . Making a change of the scale of our variables , we may evidently , and shall ...
... present theorem is shown to be a consequence of ( ii ) . The remainder of the present proof is devoted to showing that ( ii ) is valid for each fixed r . Making a change of the scale of our variables , we may evidently , and shall ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise 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 L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero