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 52
Page 2307
... boundary conditions lead to spectral operators . As our treatment of this example makes clear , it suffices to study differential operators of the simple ... BOUNDARY CONDITIONS Separated Boundary Conditions for the Second Order Operator.
... boundary conditions lead to spectral operators . As our treatment of this example makes clear , it suffices to study differential operators of the simple ... BOUNDARY CONDITIONS Separated Boundary Conditions for the Second Order Operator.
Page 2320
... boundary conditions at the outset . Suppose that if B is a boundary value , we agree to call the order of the highest derivative at 0 which appears with a non - zero coefficient in the unique expression of B in the form Bf = y , f ( 0 ) ...
... boundary conditions at the outset . Suppose that if B is a boundary value , we agree to call the order of the highest derivative at 0 which appears with a non - zero coefficient in the unique expression of B in the form Bf = y , f ( 0 ) ...
Page 2491
... boundary values at a and no boundary values at b . A common boundary condition A ( ƒ ) = 0 for all the operators 7 is imposed ; in this way , a family T , of self adjoint operators is defined . It is then established that ( 1 ) under ...
... boundary values at a and no boundary values at b . A common boundary condition A ( ƒ ) = 0 for all the operators 7 is imposed ; in this way , a family T , of self adjoint operators is defined . It is then established that ( 1 ) under ...
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