ΧΑΡΑΚΤΗΡΙΣΜΟΣ ΔΥΝΑΜΟΣΕΙΡΩΝ ΜΕ ΜΕΡΙΚΑ ΑΘΡΟΙΣΜΑΤΑ ΠΑΝΩ ΣΕ ΠΕΠΕΡΑΣΜΕΝΟ ΠΛΗΘΟΣ ΚΥΚΛΩΝ

LET K BE THE CLASS OF TRIGONOMETRIC SERIES OF POWER TYPE, I.E. TAYLOR SERIES Σ C ZN FOR Z=E IX, WHOSE PARTIAL SUMS FOR ALL X IN E, WHERE E IS A NONDENUMERABLESUBSET OF (0,2Π) LIE ON A FINITE NUMBER OF CIRCLES (A PRIORI DEPENDINGON X) IN THE COMPLEX PLANE. THE MAIN RESULT OF THIS PAPER IS THAT FOR EVERY MEMBER OF THE CLASS K, THERE EXIST A COMPLEX NUMBER Ω, /Ω/=1, AND TWO POSITIVE INTEGERS Ν,Κ, N<K, SUCH THAT FOR THE COEFFICIENTS CN WE HAVE: CΜ+Λ(Κ-Ν)=CΜΩΛ, Μ=Ν, Ν+1,...,Κ-1, Λ=1,2,3,... . THUS, EVERY MEMBER OF THE CLASS K HAS (WITH MINOR MODIFICATIONS) A REPRESENTATION OF THE FORM: P(X)Σ EIKNX, N=0 WHERE P(X) IS A SUITABLE TRIGONOMETRIC POLYNOMIAL AND K A POSITIVE INTEGER. THE PROOF IS ELEMENTARY BUT RATHER LONG. THIS RESULT IS CLOSELY RELATED TO A THEOREM OF MARCINKIEWICZ AND ZYGMUND ON THE CIRCULAR STRUCTURE OF THE SET OF LIMIT POINTS OF THE SEQUENCE OF PARTIAL SUMS OF (C,1) SUMMABLE TAYLOR SERIES.

Grantor dc:publisher

University of Crete (UOC)

Year dc:date

1988

Authors dc:creator

• Katsoprinakis, Emmanouil
• Κατσοπρινάκης, Εμμανουήλ

• ΑΘΡΟΙΣΙΜΟΤΗΤΑ CESARO
• Γωνιακή κατανομή
• ΚΥΚΛΙΚΗ ΔΟΜΗ
• ΜΕΡΙΚΑΑΘΡΟΙΣΜΑΤΑ
• Σειρές Taylor
• ΤΡΙΓΩΝΟΜΕΤΡΙΚΕΣ ΔΥΝΑΜΟΣΕΙΡΕΣ
• Angular distribution
• CESARO SUMMABILITY
• CIRCULAR STRUCTURE
• PARTIAL SUMS
• Taylor series
• TRIGONOMETRIC POWER SERIES
• Φυσικές Επιστήμες
• Μαθηματικά
• Natural Sciences
• Mathematics

Language dc:language

gre

Identifier

10.12681/eadd/0691

OAI identifier oai:identifier

oai:10442/0691