Linear Operators, Part 2 |
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Page 2307
... boundary conditions lead to spectral operators . As our treatment of this example makes clear , it suffices to study differential operators of ... BOUNDARY CONDITIONS Separated Boundary Conditions for the Second Order Operator 2290 2290 2291.
... boundary conditions lead to spectral operators . As our treatment of this example makes clear , it suffices to study differential operators of ... BOUNDARY CONDITIONS Separated Boundary Conditions for the Second Order Operator 2290 2290 2291.
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 ...
... 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 ...
Page 2517
... Boundary value and expansion problems of ordinary linear differential equa- tions . Trans . Amer . Math . Soc . 9 , 373-395 ( 1908 ) . 6. Note on the expansion of the Green's function . Math . Ann . 72 , 292-294 ( 1912 ) . 7 . Note on ...
... Boundary value and expansion problems of ordinary linear differential equa- tions . Trans . Amer . Math . Soc . 9 , 373-395 ( 1908 ) . 6. Note on the expansion of the Green's function . Math . Ann . 72 , 292-294 ( 1912 ) . 7 . Note on ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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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