Linear Operators, Part 2 |
From inside the book
Results 1-3 of 79
Page 1459
... PROOF . We use the notations of the proof of Theorem 8. By Lemma 29 and Theorem 28 it is sufficient to show that t ' is finite below 2 in order to conclude that 7 is finite below 2. But it was shown in the proof of Theorem 8 that c may ...
... PROOF . We use the notations of the proof of Theorem 8. By Lemma 29 and Theorem 28 it is sufficient to show that t ' is finite below 2 in order to conclude that 7 is finite below 2. But it was shown in the proof of Theorem 8 that c may ...
Page 1724
... PROOF . By the preceding lemma and by Corollary 11 it suffices to show that ( Tf , g ) ( f , Sg ) for f in D ( T ) and g in D ( S ) . By Green's formula , proved in the last paragraph of Section 2 , this equation is valid if ƒ and g are ...
... PROOF . By the preceding lemma and by Corollary 11 it suffices to show that ( Tf , g ) ( f , Sg ) for f in D ( T ) and g in D ( S ) . By Green's formula , proved in the last paragraph of Section 2 , this equation is valid if ƒ and g are ...
Page 1750
... proof of Theorem 1 , and shall prove it by a direct method where it is needed . Remark 2. The theorem is false if no ... PROOF ( of Theorem 1 ) . The proof will be given in a series of steps , some of which will be proofs of auxiliary ...
... proof of Theorem 1 , and shall prove it by a direct method where it is needed . Remark 2. The theorem is false if no ... PROOF ( of Theorem 1 ) . The proof will be given in a series of steps , some of which will be proofs of auxiliary ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
56 other sections not shown
Other editions - View all
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant 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 Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero