zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
The norm of minimal polynomials on several intervals. (English) Zbl 1221.41018
Author’s abstract: Using works of F. Peherstorfer, we examine how close the n-th Chebyshev number for a set E of finitely many intervals can get to the theoretical lower limit 2cap(E) n .
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
41A50Best approximation, Chebyshev systems
41A10Approximation by polynomials
[1]Bogatyrev, A. B.: Effective computation of Chebyshev polynomials for several intervals, Math. USSR sb. 190, 1571-1605 (1999) · Zbl 0986.34042 · doi:10.1070/SM1999v190n11ABEH000438
[2]Cassels, J. W. S.: An introduction to Diophantine approximation, Cambridge tracts in mathematics and mathematical physics 45 (1957) · Zbl 0077.04801
[3]Mckean, H. P.; Van Moerbeke, P.: Hill and Toda curves, Comm. pure appl. Math. 33, 23-42 (1980)
[4]Peherstorfer, F.: Deformation of minimizing polynomials and approximation of several intervals by an inverse polynomial mapping, J. approx. Theory 111, 180-195 (2001) · Zbl 1025.42014 · doi:10.1006/jath.2001.3571
[5]Peherstorfer, F.: Orthogonal and extremal polynomials on several intervals, J. comp. Appl. math. 48, 187-205 (1993) · Zbl 0790.42012 · doi:10.1016/0377-0427(93)90322-3
[6]Peherstorfer, F.: On Bernstein–Szego orthogonal polynomials on several intervals, II, J. approx. Theory 64, 123-161 (1991) · Zbl 0721.42017 · doi:10.1016/0021-9045(91)90071-H
[7]Ransford, T.: Potential theory in the complex plane, (1995)
[8]Robinson, R. M.: Conjugate algebraic integers in real point sets, Math. Z. 84, 415-427 (1964) · Zbl 0126.02902 · doi:10.1007/BF01109909
[9]Rudin, W.: Principles of mathematical analysis, (1976) · Zbl 0346.26002
[10]Saff, E. B.; Totik, V.: Logarithmic potentials with external fields, Grundlehren der mathematischen wissenschaften 316 (1997)
[11]Schiefermayr, K.: A lower bound for the minimum deviation of the Chebyshev polynomial on a compact real set, East J. Approx. 14, 65-75 (2008) · Zbl 1217.41031
[12]Sodin, M. L.; Yuditskii, P. M.: Functions that deviate least from zero on closed subsets of the real axis, St. Petersburg math. J. 4, 201-249 (1993) · Zbl 0791.41021
[13]Totik, V.: Polynomial inverse images and polynomial inequalities, Acta math. (Scandinavian) 187, 139-160 (2001) · Zbl 0997.41005 · doi:10.1007/BF02392833
[14]Totik, V.: Chebyshev constants and the inheritance problem, J. approx. Theory 160, 187-201 (2009) · Zbl 1190.41002 · doi:10.1016/j.jat.2008.08.001
[15]Widom, H.: Extremal polynomials associated with a system of curves in the complex plane, Adv. math. 3, 127-232 (1969) · Zbl 0183.07503 · doi:10.1016/0001-8708(69)90005-X