Linear Operators, Part 2 |
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Page 1393
... prove that TX is closed if TY is closed , we shall prove more generally that the sum of a closed subspace 3 of a B - space , and of a finite dimensional space îì , is closed . It is clear that proceed- ing inductively we may assume ...
... prove that TX is closed if TY is closed , we shall prove more generally that the sum of a closed subspace 3 of a B - space , and of a finite dimensional space îì , is closed . It is clear that proceed- ing inductively we may assume ...
Page 1550
... Prove that for every ( real or complex ) every solution of the equation ( 2-7 ) = 0 is of class L „ ( I ) . E9 Let T be any closed extension of the operator To ( t , p ) . Prove that the essential spectrum of T coincides with the ...
... Prove that for every ( real or complex ) every solution of the equation ( 2-7 ) = 0 is of class L „ ( I ) . E9 Let T be any closed extension of the operator To ( t , p ) . Prove that the essential spectrum of T coincides with the ...
Page 1557
... Prove that the point 2 belongs to the essential spectrum of t . G20 ( Wintner ) . Suppose that q is bounded below ... Prove that r ' is square - integrable . ( b ) Prove that ∞ f ( t ) r ' ( t ) —r ( t ) f ' ( t ) = − S °° f ( t ) r ...
... Prove that the point 2 belongs to the essential spectrum of t . G20 ( Wintner ) . Suppose that q is bounded below ... Prove that r ' is square - integrable . ( b ) Prove that ∞ f ( t ) r ' ( t ) —r ( t ) f ' ( t ) = − S °° f ( t ) r ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 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