Linear Operators, Part 2 |
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Page 1914
... problem of Theorem XV.12.21 has the kernel which defines its solution given by a fairly rapidly convergent series . The Cauchy initial value problem is , in various forms , discussed briefly in all three parts of this book , thus ...
... problem of Theorem XV.12.21 has the kernel which defines its solution given by a fairly rapidly convergent series . The Cauchy initial value problem is , in various forms , discussed briefly in all three parts of this book , thus ...
Page 1927
... problem stated for I would be : find all projections in X. This problem , while interesting in itself , clearly goes much further than a mere spectral analysis of the operator I. Indeed , since o ( I ) consists of one point only , so ...
... problem stated for I would be : find all projections in X. This problem , while interesting in itself , clearly goes much further than a mere spectral analysis of the operator I. Indeed , since o ( I ) consists of one point only , so ...
Page 2059
... problem involving the determination of the variations in lunar and solar velocities . The Babylonians not only realized the independence of these problems but developed ephemerides to solve them , and they also devised a theory which ...
... problem involving the determination of the variations in lunar and solar velocities . The Babylonians not only realized the independence of these problems but developed ephemerides to solve them , and they also devised a theory which ...
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