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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
- B. Mityagin
- 22 December 2015
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
- B. Mityagin
- 31 August 1961
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…
Bari–Markus property for Riesz projections of 1D periodic Dirac operators
The Dirac operators
Estimates for Periodic and Dirichlet Eigenvalues of the Schrödinger Operator
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…
Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators
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…