Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
From inside the book
Results 1-3 of 81
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 ) = ( c ) Prove that ( d ) ...
... 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 ) = ( c ) Prove that ( d ) ...
Page 1563
... Prove that = O ( √ ( bn - an ) ) . ( b ) Prove that the essential spectrum of 7 contains the positive semi - axis . ( Hint : Apply Theorem 7.1 . ) G41 Suppose that the function q is bounded below . Suppose that the origin belongs to ...
... Prove that = O ( √ ( bn - an ) ) . ( b ) Prove that the essential spectrum of 7 contains the positive semi - axis . ( Hint : Apply Theorem 7.1 . ) G41 Suppose that the function q is bounded below . Suppose that the origin belongs to ...
Page 1568
... Prove that the operator T1 ( t , 1 ) is closed in L1 ( 0 , ∞ ) . H15 Prove that the essential spectrum of the operator T1 ( t , 1 ) in L1 [ 0 , ∞ ) is the positive semi - axis . ( Hint : Use the method of Exercise G44 . ) H16 ...
... Prove that the operator T1 ( t , 1 ) is closed in L1 ( 0 , ∞ ) . H15 Prove that the essential spectrum of the operator T1 ( t , 1 ) in L1 [ 0 , ∞ ) is the positive semi - axis . ( Hint : Use the method of Exercise G44 . ) H16 ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
57 other sections not shown
Other editions - View all
Common terms and phrases
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