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Zinoviy Grinshpun 《Proceedings of the American Mathematical Society》2003,131(5):1591-1600
We prove the following theorem. Any isometric operator , that acts from the Hilbert space with nonnegative weight to the Hilbert space with nonnegative weight , allows for the integral representation
where the kernels and satisfy certain conditions that are necessary and sufficient for these kernels to generate the corresponding isometric operators.
where the kernels and satisfy certain conditions that are necessary and sufficient for these kernels to generate the corresponding isometric operators.
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V. Grinshpun 《Letters in Mathematical Physics》1995,34(2):103-117
We consider the lattice Schrödinger operator acting onl
2 (
d
) with random potential (independent, identically distributed random variables), supported on a subspace of dimension 1 v <d. We use the multiscale analyses scheme to prove that this operator exhibits exponential localization at the edges of the spectrum for any disorder or outside the interval [-2d, 2d] for sufficiently high disorder. 相似文献
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Zolotarev polynomials are the polynomials that have minimaldeviation from zero on [–1, 1] with respect to the norm||xn – xn–1 + an–2 xn–2 + ... + a1x+ an|| for given and for all ak . This note complements the paper of F. Pehersforfer [J. LondonMath. Soc. (1) 74 (2006) 143–153] with exact (not asymptotic)construction of the Zolotarev polynomials with respect to thenorm L1 for || < 1 and with respect to the norm L2 for || 1 in the form of Bernstein–Szegö orthogonal polynomials.For all in L1 and L2 norms, the Zolotarev polynomials satisfyexactly (not asymptotically) the triple recurrence relationof the Chebyshev polynomials. 相似文献
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Edward Grinshpun 《Integral Equations and Operator Theory》1994,19(2):240-250
LetA1 be a selfadjoint operator with discrete spectrum and known distribution function of its spectrumN(r,A). SupposeB is a (nonselfadjoint) operator that is form-bounded with respect toA with relative bound zero. If in addition
thenN(r,A+B)=N(r,A)(1+o(1)), whereA+B is the operator defined as form sum. The applications to the Schrödinger operator with polynomially growing potential and to the third boundary value problem for the second order elliptic operator are given.Research supported by the Israel Ministries of Science and Absorption 相似文献
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Zinoviy Grinshpun 《Journal of Mathematical Analysis and Applications》2004,299(1):1-18
The paper lists a number of problems that motivate consideration of special linear combinations of polynomials, orthogonal with the weight p(x) on the interval (a,b). We study properties of the polynomials, as well as the necessary and sufficient conditions for their orthogonality. The special linear combinations of Chebyshev orthogonal polynomials of four kinds with absolutely constant coefficients hold a distinguished place in the class of such linear combinations. 相似文献
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For graphs F and H, we say F is Ramsey for H if every 2‐coloring of the edges of F contains a monochromatic copy of H. The graph F is Ramsey H‐minimal if F is Ramsey for H and there is no proper subgraph of F so that is Ramsey for H. Burr et al. defined to be the minimum degree of F over all Ramsey H‐minimal graphs F. Define to be a graph on vertices consisting of a complete graph on t vertices and one additional vertex of degree d. We show that for all values ; it was previously known that , so it is surprising that is much smaller. We also make some further progress on some sparser graphs. Fox and Lin observed that for all graphs H, where is the minimum degree of H; Szabó et al. investigated which graphs have this property and conjectured that all bipartite graphs H without isolated vertices satisfy . Fox et al. further conjectured that all connected triangle‐free graphs with at least two vertices satisfy this property. We show that d‐regular 3‐connected triangle‐free graphs H, with one extra technical constraint, satisfy ; the extra constraint is that H has a vertex v so that if one removes v and its neighborhood from H, the remainder is connected. 相似文献
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Zinoviy Grinshpun 《Journal of Mathematical Analysis and Applications》2002,272(1):349-361
The paper considers the mutual relationship of oscillations of the Bernstein-Szegö orthogonal polynomials of different kinds in the boundaries that are determined by the weight functions with indication of Chebyshev's alternances. 相似文献
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