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Journals / Constructive Mathematical Analysis / 2026 / Volume: 9 Issue: 3

Non-unital semigroup of integral operators on Fock spaces

Tesfa Mengestie(Western Norway University of Applied Sciences)0000-0003-4299-7980
Pages
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Publication Date
2026-09-15
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AI Summary & Key Takeaways

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

Additionally, we compute their infinitesimal generators

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The family of Volterra-type integral operators on Fock spaces do not contain the identity operator and thus fail to form a standard one-parameter semigroup of operators.
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Key Findings & Data:By generalizing the classical definition, we introduce the notion of non-unital semigroups and characterize exactly which operators on these spaces generate such families.
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Conclusion & Impact:Additionally, we compute their infinitesimal generators
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fock space · Non-unital semigroup · Volterra-type integral

Abstract

The family of Volterra-type integral operators on Fock spaces do not contain the identity operator and thus fail to form a standard one-parameter semigroup of operators. By generalizing the classical definition, we introduce the notion of non-unital semigroups and characterize exactly which operators on these spaces generate such families. Additionally, we compute their infinitesimal generators

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Cite This Article

Mengestie, T. (2026). Non-unital semigroup of integral operators on Fock spaces. Constructive Mathematical Analysis, Volume: 9 Issue: 3. https://doi.org/10.33205/cma.1895745

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References (15)

  1. D. Applebaum: Semigroups of linear operators: with applications to analysis, probability and physics, volume 93 of London Mathematical Society Student Texts, Cambridge University Press, Cambridge (2019).
  2. E. Berkson, H. Porta: Semigroups of analytic functions and composition operators, Michigan Math. J., 25 (1978), 101–115.
  3. I. Chalendar, J. Partington: Weighted composition operators on the Fock space: iteration and semigroups, Acta Sci. Math. (Szeged), 89 (1–2) (2023), 93–108.
  4. O. Constantin: Volterra type integration operators on Fock spaces, Proc. Amer. Math. Soc., 140 (2012), 4247–4257.
  5. Z. A. Fekade, T. Mengestie and M. H. Takele: Closed Range Integral Operators on Fock Spaces, Complex Anal. Oper. Theory, 17 (2023), Article ID: 107.
  6. R. Fleming, J. Jamison: Isometries on Banach Spaces: Function Spaces, Monographs and Surveys in Pure and Applied Mathematics, vol. 129, Chapman & Hall/CRC, Boca Raton (2003).
  7. S. Li, S. Stević: Generalized composition operators on Zygmund spaces and Bloch type spaces, J. Math. Anal. Appl., 338 (2008), 1282–1295.
  8. S. Li, S. Stević: Products of Volterra type operator and composition operator from $H^{\infty}$ and Bloch spaces to the Zygmund space, J. Math. Anal. Appl., 345 (2008), 40–52.
  9. J. Manur, W. Noor and F. Santos: A weighted composition semigroup related to three open problems, J. Math. Anal. Appl, 525 (1) (2023), Article ID: 127261.
  10. T. Mengestie: Generalized Volterra Companion Operators on Fock Spaces, Potential Anal., 44 (2016), 579–599.
  11. T. Mengestie: Product of Volterra type integral and composition operators on weighted Fock spaces, J. Geom. Anal., 24 (2014), 740–755.
  12. T. Mengestie, Volterra type and weighted composition operators on weighted Fock spaces, Integr. Equ. Oper. Theory, 76 (1) (2013), 81–94.
  13. T. Mengestie, M. Worku: Topological structures of generalized Volterra-type integral operators, Mediterr. J. Math., 15 (2018), Article ID: 42.
  14. A. Pazy: Semigroups of linear operators and applications to partial differential equations, vol. 44 of Applied Mathematical Sciences. Springer-Verlag, New York (1983).
  15. J. Pau, J. A. Peláez: Embedding theorems and integration operators on Bergman spaces with rapidly decreasing weights, J. Funct. Anal., 259 (2010), 2727–2756.