Arbeitspapier
On the Decay of Infinite Products of Trigonometric Polynomials
We consider infinite products of the form ,where {mk} is an arbitrary sequence of trigonometric polynomials of degree at most n with uniformly bounded normssuch that mk(0)=1 for all k. We show that can decrease at infinity not faster than and present conditions underwhich this maximal decay attains. This result proves the impossibility of the construction of infinitely differentiablenonstationary wavelets with compact support and restricts the smoothness of nonstationary wavelets by thelength of their support. Also this generalizes well-known similar results obtained for stable sequences ofpolynomials (when all mk coincide). In several examples we show that by weakening the boundedness conditionsone can achieve an exponential decay.
- Sprache
-
Englisch
- Erschienen in
-
Series: Tinbergen Institute Discussion Paper ; No. 01-046/4
- Klassifikation
-
Wirtschaft
- Thema
-
trigonometric polynomial
infinite product
wavelets
roots
Mathematik
Theorie
- Ereignis
-
Geistige Schöpfung
- (wer)
-
Protassov, Vladimir
- Ereignis
-
Veröffentlichung
- (wer)
-
Tinbergen Institute
- (wo)
-
Amsterdam and Rotterdam
- (wann)
-
2001
- Handle
- Letzte Aktualisierung
-
10.03.2025, 11:42 MEZ
Datenpartner
Dieses Objekt wird bereitgestellt von:
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Objekttyp
- Arbeitspapier
Beteiligte
- Protassov, Vladimir
- Tinbergen Institute
Entstanden
- 2001
Ähnliche Objekte (12)
A note on some extremal problems for trigonometric polynomials
Trigonometric Bézier and Stancu Polynomials over Intervals and Triangles
Approximation and Interpolation of Singular Measures by Trigonometric Polynomials
A note on some extremal problems for trigonometric polynomials
Discrete least-norm approximation by nonnegative (trigonometric) polynomials and rational functions
Approximation by trigonometric polynomials and bandlimited functions and generalized moduli of smoothness
Positive polynomials on fibre products
Unbounded expansion of polynomials and products
Infinite families of minimal binary codes via Krawtchouk polynomials
Chapter XXVI. Convergence of infinite Series and of infinite Products.
Recursion Formulas for Integrated Products of Jacobi Polynomials
Sparse Fast Trigonometric Transforms
A note on some extremal problems for trigonometric polynomials
Trigonometric Bézier and Stancu Polynomials over Intervals and Triangles
Approximation and Interpolation of Singular Measures by Trigonometric Polynomials
A note on some extremal problems for trigonometric polynomials
Discrete least-norm approximation by nonnegative (trigonometric) polynomials and rational functions
Approximation by trigonometric polynomials and bandlimited functions and generalized moduli of smoothness
Positive polynomials on fibre products
Unbounded expansion of polynomials and products
Infinite families of minimal binary codes via Krawtchouk polynomials
Chapter XXVI. Convergence of infinite Series and of infinite Products.
Recursion Formulas for Integrated Products of Jacobi Polynomials
Sparse Fast Trigonometric Transforms
A note on some extremal problems for trigonometric polynomials
Trigonometric Bézier and Stancu Polynomials over Intervals and Triangles
Approximation and Interpolation of Singular Measures by Trigonometric Polynomials
A note on some extremal problems for trigonometric polynomials
Discrete least-norm approximation by nonnegative (trigonometric) polynomials and rational functions
Approximation by trigonometric polynomials and bandlimited functions and generalized moduli of smoothness
Positive polynomials on fibre products
Unbounded expansion of polynomials and products
Infinite families of minimal binary codes via Krawtchouk polynomials
Chapter XXVI. Convergence of infinite Series and of infinite Products.
Recursion Formulas for Integrated Products of Jacobi Polynomials