Linear Operators, Part 2 |
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Page 2227
... operators to ordinary and partial differential operators it is first necessary to extend the spectral theory of bounded operators to a theory of unbounded operators . The present chapter is an attempt to make the corresponding step in ...
... operators to ordinary and partial differential operators it is first necessary to extend the spectral theory of bounded operators to a theory of unbounded operators . The present chapter is an attempt to make the corresponding step in ...
Page 2508
... operator . In Putnam [ 27 ] it is shown that , under fairly general hypotheses , the two self adjoint operators defined by a second order ordinary differential operator on a half - axis and two different sets of end conditions are ...
... operator . In Putnam [ 27 ] it is shown that , under fairly general hypotheses , the two self adjoint operators defined by a second order ordinary differential operator on a half - axis and two different sets of end conditions are ...
Page 2537
... operators . Acta Math . 104 , 93-139 ( 1960 ) . 2. Linear partial differential operators . Springer - Verlag , Berlin , 1963 . Huige , G. E. 1. The spectral theory of some non - selfadjoint differential operators . Comm . Pure Appl ...
... operators . Acta Math . 104 , 93-139 ( 1960 ) . 2. Linear partial differential operators . Springer - Verlag , Berlin , 1963 . Huige , G. E. 1. The spectral theory of some non - selfadjoint differential operators . Comm . Pure Appl ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function 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 eigenvalues elements equation exists finite number follows from Lemma 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