SavedAdd your journal

Journals / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 3

On Wiener’s Tauberian theorems and convolution for oscillatory integral operators

Rita Correia GUERRA
Luis Pinheiro de CASTRO
Nguyen Minh TUAN
Pages
1124–1147
Publication Date
2022-11-04
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)

Additionally, a new Young-type inequality for the obtained convolution is proven, and a new Wiener-typealgebra is also associated with this convolution.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The main aim of this work is to obtain Paley–Wiener and Wiener’s Tauberian results associated withan oscillatory integral operator, which depends on cosine and sine kernels, as well as to introduce a consequent newconvolution.
📊
Key Findings & Data:The main aim of this work is to obtain Paley–Wiener and Wiener’s Tauberian results associated withan oscillatory integral operator, which depends on cosine and sine kernels, as well as to introduce a consequent newconvolution.
💡
Conclusion & Impact:Additionally, a new Young-type inequality for the obtained convolution is proven, and a new Wiener-typealgebra is also associated with this convolution.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The main aim of this work is to obtain Paley–Wiener and Wiener’s Tauberian results associated withan oscillatory integral operator, which depends on cosine and sine kernels, as well as to introduce a consequent newconvolution. Additionally, a new Young-type inequality for the obtained convolution is proven, and a new Wiener-typealgebra is also associated with this convolution.

🔖

Cite This Article

GUERRA, R. C., CASTRO, L. P. D., TUAN, N. M. (2022). On Wiener’s Tauberian theorems and convolution for oscillatory integral operators. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 3, 1124–1147. https://ajindex.com/articles/607683

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (19)

  1. Bracewell RN. The Hartley Transform. Oxford, United Kingdom: Oxford University Press, 1986
  2. Brascamp HJ, Lieb EH. Best constants in Young’s inequality, its converse, and its generalization to more than three functions. Advances in Mathematics 1976; 20: 151-173
  3. Castro LP, Guerra RC, Tuan NM. Heisenberg uncertainty principles for an oscillatory integral operator. American Institute of Physics, AIP Proc 2017; 1798(1): 020037
  4. Frank RL, Sabin J. Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces. Advances in Mathematics 2017; 317: 157-192
  5. Katznelson Y. An Introduction to Harmonic Analysis. Cambridge, UK: Cambridge University Press, 2004
  6. Korevaar J. A century of complex Tauberian theory. Bulletin of the AMS 2002; 39: 47-531
  7. Korevaar J. Tauberian Theory: A Century of Developments. Berlin, Germany: Grundl Math Wiss 329, Springer- Verlag, 2004
  8. Korevaar J. Distributional Wiener-Ikehara theorem and twin primes. Indagationes Mathematicae (NS) 2005; 16: 3-49
  9. Motygin OV. Numerical approximation of oscillatory integrals of the linear ship wave theory. Applied Numerical Mathematics 2017; 115: 99-113
  10. Novak E, Ullrich M, Woźniakowski H, Zhang S. Complexity of oscillatory integrals on the real line. Advances in Computational Mathematics 2017; 43(3): 537-553
  11. O’Neil R. Convolution operators and L(p; q) spaces. Duke Mathematical Journal 1963; 30: 129-142
  12. Pitt HR. General Tauberian theorems. Proceedings of the London Mathematical Society 1938; 44: 243-288
  13. Rudin W. Functional Analysis. New York, USA: McGraw-Hill, 1991
  14. Sjölin P. Some remarks on singular oscillatory integrals and convolution operators. Proceedings of the American Mathematical Society 2017; 145(9): 3843-3848
  15. Stein EM. Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals. New Jersey, USA: Princeton University Press, 1993
  16. Titchmarsh EC. Introduction to the Theory of Fourier Integrals. New York, USA: Chelsea Publ. Co., 1986
  17. Tuan NM, Tuan PD. Operator properties and Heisenberg uncertainty principles for a un-unitary integral operator. Integral Transforms and Special Functions 2012; 23: 1-12
  18. Veys W, Zún̈iga-Galindo WA. Zeta functions and oscillatory integrals for meromorphic functions. Advances in Mathematics 2017; 311: 295-337
  19. Xiao L. Endpoint estimates for one-dimensional oscillatory integral operators. Advances in Mathematics 2017; 316: 2