SavedAdd your journal

Journals / Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2022 / Cilt: 24 - Sayı: 2

On some properties of $W_w (IR)$ space

$W_w (IR)$ uzayının bazı özellikleri

Mevlüde DOĞAN
A. Turan GÜRKANLI
Pages
738–749
Publication Date
2022-07-08
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also, it was discussed the inclusion properties between the spaces weight function $W_{w_1} (IR)$ and $W_{w_2} (IR)$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The $W^p (IR^n )$ space and some properties of this space have been proved by Krogstad [1].
📊
Key Findings & Data:In this study, $W^p (IR^n )$ space, which is a special case for $p=1$ of this space defined by Krogstad [1], is discussed. $W_w (IR)$ is a vector space, if $w$ satisfied the Beurling-Domar condition.
💡
Conclusion & Impact:Also, it was discussed the inclusion properties between the spaces weight function $W_{w_1} (IR)$ and $W_{w_2} (IR)$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Soyut segal cebiri · ağırlık fonksiyonu · banach fonksiyon uzayı.

Abstract

The $W^p (IR^n )$ space and some properties of this space have been proved by Krogstad [1]. In this study, $W^p (IR^n )$ space, which is a special case for $p=1$ of this space defined by Krogstad [1], is discussed. $W_w (IR)$ is a vector space, if $w$ satisfied the Beurling-Domar condition. It has been proven that the $W_w (IR)$ space is a Banach space according to the $\|.\|_w$ norm defined on it. It was showed that $(W_w (IR), \|.\|_w)$ was a Banach algebra, translation invariant, strongly invariant. Moreover, it has been proved that $(W_w (IR), \|.\|_w)$ space was an abstract Segal algebra and a Banach Function space. Also, it was discussed the inclusion properties between the spaces weight function $W_{w_1} (IR)$ and $W_{w_2} (IR)$.

Özet

Wp(IRn)Wp(IRn) uzayı ve bu uzaya ait bazı özellikler Krogstad [1] tarafından ispat edilmiştir. Bu çalışmada, Krogstad tarafından tanımlanan bu uzayın p=1p=1 için özel durumu olan W(IRn)W(IRn) uzayı ele alındı. ww, IRIR reel sayılar kümesinde Beurling-Domar koşullarını sağlayan ağırlık fonksiyonu olmak üzere bir Ww(IR)Ww(IR) uzayı ve bu uzay üzerinde ∥.∥w‖.‖w normu tanımlandı. Ww(IR)Ww(IR) uzayının, ∥.∥w‖.‖w normuna göre bir Banach uzayı olduğu ispatlandı. (Ww(IR),∥.∥w)(Ww(IR),‖.‖w) uzayının bir Banach cebiri, ötelemeler altında invaryant ve kuvvetli invaryant olduğu gösterildi. Ayrıca, (Ww(IR),∥.∥w)(Ww(IR),‖.‖w) uzayının Soyut Segal cebiri ve Banach fonksiyon uzayı olduğu ispatlandı. w1w1, w2w2, IRIR üzerinde ağırlık fonksiyonları olmak üzere Ww1(IR)Ww1(IR)W(w1)(IR) ve $W_{w_2}(IR)$W(w2)(IR) uzayları arasındaki kapsama özellikleri araştırıldı.

🔖

Cite This Article

DOĞAN, M., GÜRKANLI, A. T. (2022). On some properties of $W_w (IR)$ space. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 24 - Sayı: 2, 738–749. https://ajindex.com/articles/472771

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (15)

  1. Krogstad, H.E., Multipliers of Segal algebras, Mathematica Scandinavica, 38, 285-303, (1976).
  2. Rudin, W., Real and Complex Analysis, Mc: Graw-Hill, New York, (1966).
  3. Rudin, W., Fourier analysis on groups, Interscience publishers, New-York, (1962).
  4. Reiter, H. and Stegeman, J.D., Classical harmonic analysis and locally compact groups, Clarendon Press, Oxford, (2001).
  5. Feichtinger, H.G. and Gürkanlı, A.T., On a family of weighted convolution algebras, International Journal of Mathematics and Mathematical Sciences, 13 (3), 517-526, (1990).
  6. Cartan, H., Differential calculus. Hermann, Paris, France, (1967).
  7. Wang, H.C., Homogeneous Banach algebras, Marcel Dekker INC, New York, (1977).
  8. Burnham, J.T., Closed ideals in subalgebras of Banach algebras, American Mathematical Society, 32 (2), 551-555, (1972).
  9. Bennett, C. and Sharpley, R., Interpolation of Operators, Academic Press,
  10. San Diego, USA, (1988).
  11. Domar, Y., Harmonic analysis based on certain commutative banach algebras, Acta Mathematica, 96, 1-66, (1956).
  12. Beurling, A., Sur les integrales de fourier absolument convergentes. IX. Scandinavian Mathematical Congress, Helsingfors, (1938).
  13. Fischer, R.H., Gürkanlı, A.T. and Liu, T.S., On family of weighted spaces and Wiener type spaces Mathematica Slovaca, 46 (1), 71-82, (1996).
  14. Numan, S., A_w (p,q)(G) Banach cebirinin idealleri, Karadeniz Fen Bilimleri Dergisi, 10 (1), 162-177, (2020).
  15. Sağır, B., On functions with Fourier transforms in W(B,Y), Demonstratio Mathematica, 33 (2), 355-363, (2000).