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Uniform embeddings of metric spaces and of banach spaces into hilbert spaces
It is proved using positive definite functions that a normed spaceX is unifomly homeomorphic to a subset of a Hilbert space, if and only ifX is (linearly) isomorphic to a subspace of aL0(μ) spaceExpand
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APPROXIMATE DIMENSION AND BASES IN NUCLEAR SPACES
CONTENTSIntroduction § 1. The concept of nuclearity and the simplest facts connected with it § 2. Approximative dimension: the estimation of the e-entropy and n-dimensional diameter of elementaryExpand
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The Zero Set of a Real Analytic Function
A brief proof of the statement that the zero-set of a nontrivial real-analytic function in $d$-dimensional space has zero measure is provided.
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Estimates for Periodic and Dirichlet Eigenvalues of the Schrödinger Operator
Consider the Schrodinger equation $-y' + Vy = \lambda y$ for a complex-valued potential V of period 1 in the weighted Sobolev space $H^w$ of 2-periodic functions $f : \mathbb R \rightarrow \mathbbExpand
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Unconditional convergence of spectral decompositions of 1D Dirac operators with regular boundary conditions
One-dimensional Dirac operators L-bc(v)y = i(1 0 0 -1) dy/dx + v(x)y, y = (y(1)y(2)), x is an element of [0, pi], considered with L-2-potentials v (x) = (0 Q(x) P(x)0) and subject to regularExpand
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Instability zones of periodic 1-dimensional Schrödinger and Dirac operators
The spectra of Schrodinger and Dirac operators with periodic potentials on the real line have a band structure, that is, the intervals of continuous spectrum alternate with spectral gaps, orExpand
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Bari-Markus property for Riesz projections of 1D periodic Dirac operators
The Dirac operators Ly = i ((1)(0) (0)(-1))dy/dx + v(x)y, y = ((y1)(y2)), x is an element of[0, pi], with L-2-potentials v(x) = ((0)(Q(x)) (P(x))(0)), P, Q is an element of L-2([0, pi]),Expand
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Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators
We study the system of root functions (SRF) of Hill operator $Ly = -y^{\prime \prime} +vy $ with a singular potential $v \in H^{-1}_{per}$ and SRF of 1D Dirac operator $ Ly = i {pmatrix} 1 & 0 0 & -1Expand
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Eigensystem of an L2-perturbed harmonic oscillator is an unconditional basis
For any complex valued Lp-function b(x), 2 ≤ p < ∞, or L∞-function with the norm ‖b↾L∞‖ < 1, the spectrum of a perturbed harmonic oscillator operator L = −d2/dx2 + x2 + b(x) in L2(ℝ1) is discrete andExpand
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