Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1074
... transform of a function in ∞ ) , the Fourier transforms being defined as in Exercise 6 . 10 Let λ be a function defined on ( ∞ , ∞ ) which is of finite total variation . Show that if 1 < p ≤ 2 , and if F is the Fourier transform of ...
... transform of a function in ∞ ) , the Fourier transforms being defined as in Exercise 6 . 10 Let λ be a function defined on ( ∞ , ∞ ) which is of finite total variation . Show that if 1 < p ≤ 2 , and if F is the Fourier transform of ...
Page 1178
... transform ( § ) into the vector - valued function whose nth component has the Fourier transform h ( ) defined by ( 61 ) h2 ( § ) = g ( § ) , 2 " < | < 2 " + 1 , = = 0 , otherwise . By Corollary 24 , M is a bounded linear transformation ...
... transform ( § ) into the vector - valued function whose nth component has the Fourier transform h ( ) defined by ( 61 ) h2 ( § ) = g ( § ) , 2 " < | < 2 " + 1 , = = 0 , otherwise . By Corollary 24 , M is a bounded linear transformation ...
Page 1271
... transform can be used to determine when a symmetric operator has a self adjoint extension . Let T be a sym- metric operator with domain D ( T ) dense in H. Then if x is in D ( T ) , we have ( Til ) x2 = ( Tx , Tx ) i ( x , Tx ) + i ( Tx ...
... transform can be used to determine when a symmetric operator has a self adjoint extension . Let T be a sym- metric operator with domain D ( T ) dense in H. Then if x is in D ( T ) , we have ( Til ) x2 = ( Tx , Tx ) i ( x , Tx ) + i ( Tx ...
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