Published/Accepted Articles

[12] G. Debruyne, D. Seifert, Optimality of the quantified Ingham-Karamata theorem for operator semigroups with general resolvent growth, Arch. Math., accepted. [Preprint]

[11] G. Debruyne, F. Maes, J. Vindas, Halász's theorem for Beurling generalized numbers, Acta Arith., accepted. [Preprint]

[10] G. Debruyne, D. Seifert, An abstract approach to optimal decay of functions and operator semigroups, Israel J. Math., accepted. [Article|Preprint]

[9] G. Debruyne, J. Vindas, Complex Tauberian theorems for Laplace transforms with local pseudofunction boundary behavior, J. Anal. Math., 138 (2019), 799-833. [Article|Preprint]

[8] G. Debruyne, J. Vindas, On Diamond's L^1 criterion for asymptotic density of Beurling generalized integers, Michigan Math. J. 68 (2019), 211-223. [Article|Preprint]

[7] G. Debruyne, J. Vindas, Note on the absence of remainders in the Wiener-Ikehara theorem, Proc. Amer. Math. Soc. 146 (2018), 5097-5103. [Article|Preprint]

[6] G. Debruyne, J. Vindas, Optimal Tauberian constant in Ingham's theorem for Laplace transforms, Israel J. Math. 228 (2018), 557-586. [Article|Preprint]

[5] G. Debruyne, H.G. Diamond, J. Vindas, M(x)=o(x) Estimates for Beurling numbers, J. Théor. Nombres Bordeaux 30 (2018), 469-483. [Article|Preprint]

[4] G. Debruyne, J. Vindas, On PNT equivalences for Beurling numbers, Monatsh. Math. 184 (2017), 401-424. [Article|Preprint]

[3] G. Debruyne, J. Vindas, On general prime number theorems with remainder, in: Generalized Functions and Fourier Analysis, pp. 79-94. Oper. Theory Adv. Appl., Vol. 260, Springer, 2017. [Article|Preprint]

[2] G. Debruyne, J. Vindas, Generalization of the Wiener-Ikehara theorem, Illinois J. Math. 60 (2016), 613-624. [Article|Preprint]

[1] G. Debruyne, J.-C. Schlage-Puchta, J. Vindas, Some examples in the theory of Beurling's generalized prime numbers, Acta Arith. 176 (2016), 101-129. [Article|Preprint]

Ph.D Thesis

G. Debruyne, Complex Tauberian theorems and applications to Beurling generalized primes, Dissertation, Ghent University, Ghent, Belgium, 2018 [pdf]