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Page 996
... Lemma 3.1 ( d ) it follows from the above equation that f * q0 . From Lemma 12 ( b ) it is seen that o ( ƒ * q ) ≤ o ( p ) and from Lemma 12 ( c ) and the equation f = tf it follows that o ( ƒ * q ) contains no interior point of o ( q ) ...
... Lemma 3.1 ( d ) it follows from the above equation that f * q0 . From Lemma 12 ( b ) it is seen that o ( ƒ * q ) ≤ o ( p ) and from Lemma 12 ( c ) and the equation f = tf it follows that o ( ƒ * q ) contains no interior point of o ( q ) ...
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 f 1/4 belongs to Am + ( 1/4 ) . Thus ( cf. 3.48 ) fg belongs to Am + ) ( 4 ) , and the proof of Lemma 3 is complete . Q.E.D. π = PROOF ( OF THEOREM 2 ) . Let J be a domain whose ...
... follows from Lemmas 3.9 and 3.23 that the restriction f 1/4 belongs to Am + ( 1/4 ) . Thus ( cf. 3.48 ) fg belongs to Am + ) ( 4 ) , and the proof of Lemma 3 is complete . Q.E.D. π = PROOF ( OF THEOREM 2 ) . Let J be a domain whose ...
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BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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