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Asymptotic properties of polynomials with auxiliary conditions of interpolation

Author: J L Walsh; Harvard University.; United States. Air Force. Office of Scientific Research.
Publisher: Washington, D.C. : Mathematical Sciences Directorates, Air Force Office of Scientific Research, 1961.
Series: United States. Air Force Office of Scientific Research, AFOSR 9.
Edition/Format:   Print book : National government publication : EnglishView all editions and formats
Summary:
Let a closed bounded point set E be given in the z-plane. Necessary and sufficient conditions are found for validity of the following: given assigned conditions of interpolation in a finite number of points: pn(zk) = Ank; there exists a sequence of polynomials pn(z) satisfying these conditions and lim sup max pn(z), z on E 1/n = (E), where (E) is the transfinite diameter of E. (Author).
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Additional Physical Format: Online version:
Walsh, J. L. (Joseph Leonard), 1895-1973.
Asymptotic properties of polynomials with auxiliary conditions of interpolation
(OCoLC)1103291287
Material Type: Government publication, National government publication
Document Type: Book
All Authors / Contributors: J L Walsh; Harvard University.; United States. Air Force. Office of Scientific Research.
OCLC Number: 227262150
Notes: Date of Report: April, 1961.
Contract numbers: AF 49(638)-574 and AF 49(638)-845.
Description: 15 pages ; 28 cm.
Series Title: United States. Air Force Office of Scientific Research, AFOSR 9.
Other Titles: Technical Report Archive & Image Library (TRAIL)
Responsibility: J.L. Wash, Harvard University.

Abstract:

Let a closed bounded point set E be given in the z-plane. Necessary and sufficient conditions are found for validity of the following: given assigned conditions of interpolation in a finite number of points: pn(zk) = Ank; there exists a sequence of polynomials pn(z) satisfying these conditions and lim sup max pn(z), z on E 1/n = (E), where (E) is the transfinite diameter of E. (Author).

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