Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 984
... vanishes in a neighborhood of infinity is dense in L1 ( R ) . → PROOF . It follows from Lemma 3.6 that the set of all functions in L2 ( R , B , μ ) which vanish outside of compact sets is dense in this space , and from the Plancherel ...
... vanishes in a neighborhood of infinity is dense in L1 ( R ) . → PROOF . It follows from Lemma 3.6 that the set of all functions in L2 ( R , B , μ ) which vanish outside of compact sets is dense in this space , and from the Plancherel ...
Page 997
... vanishes on U for every f in L1 ( R ) ~ L2 ( R ) whose transform vanishes on the complement of V. PROOF . If moo ( q ) then there is a neighborhood V of the identity in R and a neighborhood U of m , such that U ( o ( 9 ) + V + V ) is ...
... vanishes on U for every f in L1 ( R ) ~ L2 ( R ) whose transform vanishes on the complement of V. PROOF . If moo ( q ) then there is a neighborhood V of the identity in R and a neighborhood U of m , such that U ( o ( 9 ) + V + V ) is ...
Page 1650
... vanishes in each set I , it vanishes in Uala PROOF . The proofs of the first four parts of this lemma are left to the reader as an exercise . = 0 To prove ( v ) , we must show from our hypothesis that F ( q ) if q is in Co ( Uala ) ...
... vanishes in each set I , it vanishes in Uala PROOF . The proofs of the first four parts of this lemma are left to the reader as an exercise . = 0 To prove ( v ) , we must show from our hypothesis that F ( q ) if q is in Co ( Uala ) ...
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