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Uniform embeddings of metric spaces and of banach spaces into hilbert spaces

- I. Aharoni, B. Maurey, B. Mityagin
- Mathematics
- 1 December 1985

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… Expand

73 13

APPROXIMATE DIMENSION AND BASES IN NUCLEAR SPACES

- B. Mityagin
- Mathematics
- 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… Expand

170 10

The Zero Set of a Real Analytic Function

- B. Mityagin
- Mathematics
- 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.

75 8- PDF

Estimates for Periodic and Dirichlet Eigenvalues of the Schrödinger Operator

- T. Kappeler, B. Mityagin
- Mathematics, Computer Science
- SIAM J. Math. Anal.
- 2001

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 \mathbb… Expand

51 7- PDF

Unconditional convergence of spectral decompositions of 1D Dirac operators with regular boundary conditions

- P. Djakov, B. Mityagin
- Mathematics
- 24 August 2010

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… Expand

42 6- PDF

Instability zones of periodic 1-dimensional Schrödinger and Dirac operators

- P. Djakov, B. Mityagin
- Mathematics
- 31 August 2006

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… Expand

96 5

Bari-Markus property for Riesz projections of 1D periodic Dirac operators

- P. Djakov, B. Mityagin
- Mathematics
- 7 January 2009

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

43 5- PDF

Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators

- P. Djakov, B. Mityagin
- Mathematics
- 28 June 2011

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 & -1… Expand

63 5- PDF

Eigensystem of an L2-perturbed harmonic oscillator is an unconditional basis

- J. Adduci, B. Mityagin
- Mathematics, Physics
- 14 December 2009

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… Expand

31 4- PDF

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