Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 84
Page 1086
... Moreover , the series D ( s , t ; 2 ) - ∞ ( -2 ) " Σ D ( s , t ) n = 2 ( n - 1 ) ! converges for all λ , for μμ - almost all [ s , t ] , and D ( s , t ; λ ) is the kernel which represents the operator D ( λ ) —λd ( 2 ) I of the ...
... Moreover , the series D ( s , t ; 2 ) - ∞ ( -2 ) " Σ D ( s , t ) n = 2 ( n - 1 ) ! converges for all λ , for μμ - almost all [ s , t ] , and D ( s , t ; λ ) is the kernel which represents the operator D ( λ ) —λd ( 2 ) I of the ...
Page 1093
... Moreover | T1T2r ≤ 21 / " | T1 \ ,, Talr , 2r 0 < r < ∞ . ( d ) If T is in C , and A is bounded , then AT and TA are in C ,; moreover , | AT | , ≤ | A || T | ,; \ TA \ , ≤ \ T \ , | A | . ( e ) C2 is the Hilbert - Schmidt class of ...
... Moreover | T1T2r ≤ 21 / " | T1 \ ,, Talr , 2r 0 < r < ∞ . ( d ) If T is in C , and A is bounded , then AT and TA are in C ,; moreover , | AT | , ≤ | A || T | ,; \ TA \ , ≤ \ T \ , | A | . ( e ) C2 is the Hilbert - Schmidt class of ...
Page 1688
... Moreover , there is a constant K depending on I , q , p , k , n , but not on † , such that If 1/4 dx ≤ ล dx J≤k 1 p n then we have lim ess sup f ( x ) − f ( x ) | = 0 . M → ∞ xe I Moreover , there exists a constant K depending on I ...
... Moreover , there is a constant K depending on I , q , p , k , n , but not on † , such that If 1/4 dx ≤ ล dx J≤k 1 p n then we have lim ess sup f ( x ) − f ( x ) | = 0 . M → ∞ xe I Moreover , there exists a constant K depending on I ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
37 other sections not shown
Other editions - View all
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 Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero