Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 14
Page 867
... Cauchy sequence in X / 3 and л , ex „ , n = 1 , 2 , . . .. Choose a subsequence { x } such that 1 + 1 < ∞ . Fix 1 ... sequence y1 = x + , is then a Cauchy sequence , for p - 1 │Yn + p Yn = Σ Yn + k + 1 ― Yn + k k = 0 p - 1 ≤ΣYn + x + ...
... Cauchy sequence in X / 3 and л , ex „ , n = 1 , 2 , . . .. Choose a subsequence { x } such that 1 + 1 < ∞ . Fix 1 ... sequence y1 = x + , is then a Cauchy sequence , for p - 1 │Yn + p Yn = Σ Yn + k + 1 ― Yn + k k = 0 p - 1 ≤ΣYn + x + ...
Page 1187
... Cauchy sequence in D ( B ) then { [ x , Bxn ] } is a Cauchy sequence in the closed set ( B ) and hence it has a limit [ x , Bx ] in T ( B ) . Thus the sequence { x } converges to the point a in D ( B ) which proves that D ( B ) is ...
... Cauchy sequence in D ( B ) then { [ x , Bxn ] } is a Cauchy sequence in the closed set ( B ) and hence it has a limit [ x , Bx ] in T ( B ) . Thus the sequence { x } converges to the point a in D ( B ) which proves that D ( B ) is ...
Page 1422
... Cauchy sequence . If x is its limit , it is clear since S is closed that xe D ( S ) , and ( S + uil ) x 2 . == Let y ... sequence of real numbers approaching from below . By [ ft ] , R ( —μ „ i ; S ) | ≤ μ‚1 . It follows from Lemma XII ...
... Cauchy sequence . If x is its limit , it is clear since S is closed that xe D ( S ) , and ( S + uil ) x 2 . == Let y ... sequence of real numbers approaching from below . By [ ft ] , R ( —μ „ i ; S ) | ≤ μ‚1 . It follows from Lemma XII ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Copyright | |
29 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers 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 subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero