Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
From inside the book
Results 1-3 of 75
Page 996
... Lemma 3.1 ( d ) it follows from the above equation that f * 90 . From Lemma 12 ( b ) it is seen that o ( f * q ) Co ( q ) and from Lemma 12 ( c ) and the equation tƒ = tf it follows that o ( f * q ) contains no interior point of o ( y ) ...
... Lemma 3.1 ( d ) it follows from the above equation that f * 90 . From Lemma 12 ( b ) it is seen that o ( f * q ) Co ( q ) and from Lemma 12 ( c ) and the equation tƒ = tf it follows that o ( f * q ) contains no interior point of o ( y ) ...
Page 1226
... follows immediately from part ( a ) and Lemma 5 ( c ) . Q.E.D. It follows from Lemma 6 ( b ) that any symmetric operator with dense domain has a unique minimal closed symmetric extension . This fact leads us to make the following ...
... follows immediately from part ( a ) and Lemma 5 ( c ) . Q.E.D. It follows from Lemma 6 ( b ) that any symmetric operator with dense domain has a unique minimal closed symmetric extension . This fact leads us to make the following ...
Page 1708
... follows from Lemmas 3.9 and 3.23 that the restriction fel 1/4 belongs to Am + ( 1/4 ) . Thus ( cf. 3.48 ) f / 4 belongs to Am + P ) ( 4 ) , and the proof of Lemma 3 is complete . Q.E.D. PROOF ( OF THEOREM 2 ) . Let J be a domain whose ...
... follows from Lemmas 3.9 and 3.23 that the restriction fel 1/4 belongs to Am + ( 1/4 ) . Thus ( cf. 3.48 ) f / 4 belongs to Am + P ) ( 4 ) , and the proof of Lemma 3 is complete . Q.E.D. PROOF ( OF THEOREM 2 ) . Let J be a domain whose ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
25 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 Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain 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 isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero