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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) space
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.
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 elementary
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 regular
Estimates for Periodic and Dirichlet Eigenvalues of the Schrödinger Operator
TLDR
For any 1-periodic potential V in H^w, the Schrodinger equation for a complex-valued potential V of period 1 in the weighted Sobolev space is rewritten as follows:.
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, or
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 and
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