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Yıl 2023, Cilt: 6 Sayı: 3, 128 - 134, 17.09.2023

Effie Oyugi Job Bonyo , David Ambogo

https://doi.org/10.33434/cams.1298613

Öz

Kaynakça

  • [1] K. Zhu, Operator Theory in function spaces, Mathematical Surveys and Monographs, 138, American Mathematical Society, Providence, (2007).
  • [2] O. El-Fallah, K. Kellay, J. Mashreghi, T. Ransford, A primer on the Dirichlet Space, Cambridge University Press, New York, 203, (2014).
  • [3] M. M. Peloso, Classical Spaces of Holomorphic Functions Technical report, Universit di Milano, (2014).
  • [4] J. M. Wanjiru, J. O. Bonyo, I. S. Wattanga, Reproducing Kernel for the Classical Dirichlet Space of the Upper Half Plane, IJFSCFRT, 15, (2022), 150-161.
  • [5] K. Engel, R. Nagel, A Short Course on Operator Semigroups, Universitext, Springer, New York, 37, (2006).
  • [6] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1970.
  • [7] A. G. Siskakis, Semigroups of composition operators on the spaces of analytic functions, a review, Contemp. Math., 213, (1998), 229-252.
  • [8] R. K. Singh, J. S. Manhas, Composition operators on functional spaces. Elsevier Science Publishers, Amsterdam, 179, 1993. s3-10(1), (1960), 376-394.
  • [9] A. G. Siskakis, Semigroups of composition operators on Dirichlet spaces, Results Math., 30, (1996), 165-173.
  • [10] A. G. Arvanitidis, A. G. Siskasis, Ces`aro Operators on the Hardy spaces of the half-plane, Canad. Math. Bull., 56(2), (2013), 229-240.
  • [11] S. Ballamoole, J. O. Bonyo, T. L. Miller, V. G. Miller, Ces`aro Operators on the Hardy and Bergman spaces of the half-plane, Complex Anal. Oper. Theory, 10, (2016), 187-203.
  • [12] M. O. Agwang, J. O. Bonyo, Spectra of composition groups on the weighted Dirichlet space of the upper half plane, Acta Math. Sci., 40B(6), (2020), 1739-1752.

Ces\`{a}ro-Type Operator on the Dirichlet Space of the Upper Half Plane

Yıl 2023, Cilt: 6 Sayı: 3, 128 - 134, 17.09.2023

Effie Oyugi Job Bonyo , David Ambogo

https://doi.org/10.33434/cams.1298613

Öz

We construct a Ces\`{a}ro-type operator acting on Dirichlet space of the upper half plane using the approach of strongly continuous semigroups of composition operators on Banach spaces. We then determine the spectral and norm properties of the obtained Ces\`{a}ro-type operator.

Anahtar Kelimeler

Ces\`{a}ro-type operator Generator One-parameter semigroup Resolvent Spectrum

Kaynakça

  • [1] K. Zhu, Operator Theory in function spaces, Mathematical Surveys and Monographs, 138, American Mathematical Society, Providence, (2007).
  • [2] O. El-Fallah, K. Kellay, J. Mashreghi, T. Ransford, A primer on the Dirichlet Space, Cambridge University Press, New York, 203, (2014).
  • [3] M. M. Peloso, Classical Spaces of Holomorphic Functions Technical report, Universit di Milano, (2014).
  • [4] J. M. Wanjiru, J. O. Bonyo, I. S. Wattanga, Reproducing Kernel for the Classical Dirichlet Space of the Upper Half Plane, IJFSCFRT, 15, (2022), 150-161.
  • [5] K. Engel, R. Nagel, A Short Course on Operator Semigroups, Universitext, Springer, New York, 37, (2006).
  • [6] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1970.
  • [7] A. G. Siskakis, Semigroups of composition operators on the spaces of analytic functions, a review, Contemp. Math., 213, (1998), 229-252.
  • [8] R. K. Singh, J. S. Manhas, Composition operators on functional spaces. Elsevier Science Publishers, Amsterdam, 179, 1993. s3-10(1), (1960), 376-394.
  • [9] A. G. Siskakis, Semigroups of composition operators on Dirichlet spaces, Results Math., 30, (1996), 165-173.
  • [10] A. G. Arvanitidis, A. G. Siskasis, Ces`aro Operators on the Hardy spaces of the half-plane, Canad. Math. Bull., 56(2), (2013), 229-240.
  • [11] S. Ballamoole, J. O. Bonyo, T. L. Miller, V. G. Miller, Ces`aro Operators on the Hardy and Bergman spaces of the half-plane, Complex Anal. Oper. Theory, 10, (2016), 187-203.
  • [12] M. O. Agwang, J. O. Bonyo, Spectra of composition groups on the weighted Dirichlet space of the upper half plane, Acta Math. Sci., 40B(6), (2020), 1739-1752.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Effie Oyugi 0009-0003-5820-7362

Job Bonyo 0000-0002-6442-4211

David Ambogo 0000-0003-0757-0615

Erken Görünüm Tarihi 12 Eylül 2023
Yayımlanma Tarihi 17 Eylül 2023
Gönderilme Tarihi 17 Mayıs 2023
Kabul Tarihi 21 Ağustos 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 3

Kaynak Göster

APA Oyugi, E., Bonyo, J., & Ambogo, D. (2023). Ces\`{a}ro-Type Operator on the Dirichlet Space of the Upper Half Plane. Communications in Advanced Mathematical Sciences, 6(3), 128-134. https://doi.org/10.33434/cams.1298613
AMA Oyugi E, Bonyo J, Ambogo D. Ces\`{a}ro-Type Operator on the Dirichlet Space of the Upper Half Plane. Communications in Advanced Mathematical Sciences. Eylül 2023;6(3):128-134. doi:10.33434/cams.1298613
Chicago Oyugi, Effie, Job Bonyo, ve David Ambogo. “Ces\`{a}ro-Type Operator on the Dirichlet Space of the Upper Half Plane”. Communications in Advanced Mathematical Sciences 6, sy. 3 (Eylül 2023): 128-34. https://doi.org/10.33434/cams.1298613.
EndNote Oyugi E, Bonyo J, Ambogo D (01 Eylül 2023) Ces\`{a}ro-Type Operator on the Dirichlet Space of the Upper Half Plane. Communications in Advanced Mathematical Sciences 6 3 128–134.
IEEE E. Oyugi, J. Bonyo, ve D. Ambogo, “Ces\`{a}ro-Type Operator on the Dirichlet Space of the Upper Half Plane”, Communications in Advanced Mathematical Sciences, c. 6, sy. 3, ss. 128–134, 2023, doi: 10.33434/cams.1298613.
ISNAD Oyugi, Effie vd. “Ces\`{a}ro-Type Operator on the Dirichlet Space of the Upper Half Plane”. Communications in Advanced Mathematical Sciences 6/3 (Eylül 2023), 128-134. https://doi.org/10.33434/cams.1298613.
JAMA Oyugi E, Bonyo J, Ambogo D. Ces\`{a}ro-Type Operator on the Dirichlet Space of the Upper Half Plane. Communications in Advanced Mathematical Sciences. 2023;6:128–134.
MLA Oyugi, Effie vd. “Ces\`{a}ro-Type Operator on the Dirichlet Space of the Upper Half Plane”. Communications in Advanced Mathematical Sciences, c. 6, sy. 3, 2023, ss. 128-34, doi:10.33434/cams.1298613.
Vancouver Oyugi E, Bonyo J, Ambogo D. Ces\`{a}ro-Type Operator on the Dirichlet Space of the Upper Half Plane. Communications in Advanced Mathematical Sciences. 2023;6(3):128-34.
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