zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Non-symmetric fast decreasing polynomials and applications. (English) Zbl 1254.41007
From the authors abstract: A polynomial P n is called fast decreasing if P n (0)=1, and, on [-1,1], P n decreases fast (in terms of n and the distance from 0) as we move away from the origin. This paper considers the version in which P n decreases only on some non-symmetric interval [-a,1] with possibly small a. In this case, one gets a faster decrease, and this type of extension is needed in some problems, when symmetric fast decreasing polynomials are not sufficient. Such non-symmetric fast decreasing polynomials are applied to find local bounds for Christoffel functions and for local zero spacing of orthogonal polynomials with respect to a doubling measure close to a local endpoint.
MSC:
41A10Approximation by polynomials
References:
[1]Devore, R. A.; Lorentz, G. G.: Constructive approximation, Grundlehren der mathematischen wissenschaften 303 (1993) · Zbl 0797.41016
[2]Freud, G.: Orthogonal polynomials, (1971) · Zbl 0226.33014 · doi:10.1007/BF01094355
[3]Ivanov, K. G.; Totik, V.: Fast decreasing polynomials, Constr. approx. 6, 1-20 (1990) · Zbl 0682.41014 · doi:10.1007/BF01891406
[4]Last, Y.; Simon, B.: Fine structure of the zeros of orthogonal polynomials, IV: a priori bounds and clock behavior, Comm. pure appl. Math. 61, 486-538 (2008) · Zbl 1214.42044 · doi:10.1002/cpa.20185
[5]Mastroianni, G.; Totik, V.: Weighted polynomial inequalities with doubling and A weights, Constr. approx. 16, No. 1, 37-71 (2000) · Zbl 0956.42001 · doi:10.1007/s003659910002
[6]Mastroianni, G.; Totik, V.: Uniform spacing of zeros of orthogonal polynomials, Constr. approx. 32, No. no. 2, 181-192 (2010) · Zbl 1205.42027 · doi:10.1007/s00365-009-9047-1
[7]Nevai, P.: Géza freud, orthogonal polynomials and Christoffel functions. A case study, J. approx. Theory 48, 1-167 (1986) · Zbl 0606.42020 · doi:10.1016/0021-9045(86)90016-X
[8]Ransford, T.: Potential theory in the complex plane, (1995)
[9]Simon, B.: Weak convergence of CD kernels and applications, Duke math. J. 146, 305-330 (2009) · Zbl 1158.33003 · doi:10.1215/00127094-2008-067
[10]Stahl, H.; Totik, V.: General orthogonal polynomials, Encyclopedia of mathematics and its applications 43 (1992) · Zbl 0791.33009
[11]Totik, V.: The inheritance problem and monotone systems, Austral. math. Soc. gaz. 33, 122-130 (2006)
[12]T. Varga, Uniform spacing of zeros of orthogonal polynomials for locally doubling measures (manuscript).