Linear Operators, Part 2 |
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Page 926
... gives a concise account of both the bounded and unbounded cases , as does the more recent work of Riesz and Sz ... give only very brief remarks concerning the results presented in the text . This will enable us to comment on various ...
... gives a concise account of both the bounded and unbounded cases , as does the more recent work of Riesz and Sz ... give only very brief remarks concerning the results presented in the text . This will enable us to comment on various ...
Page 1163
... gives related results dealing with the product of an arbitrary finite number of operators of Hilbert - Schmidt type . Nikovič [ 1 ] gives some results for a class of integral operators defined by requiring the finiteness of integral ...
... gives related results dealing with the product of an arbitrary finite number of operators of Hilbert - Schmidt type . Nikovič [ 1 ] gives some results for a class of integral operators defined by requiring the finiteness of integral ...
Page 1306
... gives the the number of boundary values for v in each of the cases ( i ) – ( iv ) above . Number of linearly independent boundary values for 7 : ( i ) ( ii ) ( iii ) ( iv ) At a 2 020 At b 2 2 0 0 τ In H. Weyl's terminology we say that ...
... gives the the number of boundary values for v in each of the cases ( i ) – ( iv ) above . Number of linearly independent boundary values for 7 : ( i ) ( ii ) ( iii ) ( iv ) At a 2 020 At b 2 2 0 0 τ In H. Weyl's terminology we say that ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 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