Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
From inside the book
Results 1-3 of 56
Page 2051
... consider the problem of finding the explicit form of the solu- tion to the Cauchy problem whose existence is established in Theorem 19 . As before , we assume that a2t > 0 . It follows from equation ( 55 ) which gives the analytical ...
... consider the problem of finding the explicit form of the solu- tion to the Cauchy problem whose existence is established in Theorem 19 . As before , we assume that a2t > 0 . It follows from equation ( 55 ) which gives the analytical ...
Page 2409
... considering the space L2 ( D ) as above , we may consider the space L , ( D , X ) of all X - valued Borel - Lebesgue measurable functions defined in D and satisfying ( 33 ) 1 / p { √2 If ( x , y ) dx dy 1 } " = { √ √ √ ( = ) P ...
... considering the space L2 ( D ) as above , we may consider the space L , ( D , X ) of all X - valued Borel - Lebesgue measurable functions defined in D and satisfying ( 33 ) 1 / p { √2 If ( x , y ) dx dy 1 } " = { √ √ √ ( = ) P ...
Page 2488
... Consider A self adjoint , and expand in the eigenvectors of A. ) 17 ( a ) Let f be a continuous function of bounded variation on an interval [ a , b ] , and let V ( ƒ ) denote its total variation . Show that ( x ) dx ≤ 2 max | ƒ ( x ) ...
... Consider A self adjoint , and expand in the eigenvectors of A. ) 17 ( a ) Let f be a continuous function of bounded variation on an interval [ a , b ] , and let V ( ƒ ) denote its total variation . Show that ( x ) dx ≤ 2 max | ƒ ( x ) ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
23 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero