Gergely Kiss's recent papers

Spectral analysis and synthesis on Abelian groups

Application to Functional equations



• Linear functional equations with algebraic parameters, Publ. Math. Debrecen 85, (2014), no.1-2 (pdf-file)


• Existence of nontrivial solutions of linear functional equations, (with A. Varga), Aequat. Math. 88, (2013), 151-162. (pdf-file)


• Linear functional equations, differential operators and spectral synthesis, (with M. Laczkovich), Aequat. Math. 89 (2), (2015), 301-328. (pdf-file)


• Algebraic methods for the solution of linear functional equations, (with A. Varga, Cs. Vincze), Acta Math. Hungar. 146 (1), (2015), 128-141. (pdf-file)


• Linear functional equations (Ph. D. abstract), Annales Univ. Sci. Budapest, 58 (2015), 125-132. (pdf-file)


• On spectral analysis in varieties containing the solutions of inhomogeneous linear functional equations, (with Cs. Vincze), Aequat. Math. 91 (4), (2017), 663-690. (pdf-file)


• On spectral synthesis in varieties containing the solutions of inhomogeneous linear functional equations, (with Cs. Vincze), Aequat. Math. 91 (4), (2017), 691-723. (pdf-file)


• On functional equations characterizing derivations: methods and examples, (with E. Gselmann, Cs. Vincze), Results in Mathematics (2018), doi.org/10.1007/s00025-018-0833-6. (pdf-file)


• Derivations and differential operators on rings and fields, (with M. Laczkovich), accepted at Annales Univ. Sci. Budapest, (2018). (pdf-file)


• Characterization of field homomorphisms through Pexiderized functional equations, (with E. Gselmann, Cs. Vincze), submitted to Journal of Difference Equations and Applications (pdf-file)



Pompeiu and Fuglede problem



• The discrete Pompeiu problem on the plane, (with M. Laczkovich, Cs. Vincze), Monatshefte fur Matematik 186 (2), (2018), 299-314.(pdf-file)


• On discrete Pompeiu and Fuglede problem, (with R. Malikiosis, G. Somlai, M. Vizer), submitted to Analysis & PDE, (pdf-file)



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Other topics of research

Fractal geometry



• How large dimension guarantees a given angle? (with V. Harangi, T. Keleti, P. Maga, A. Mathe, P. Mattila, B. Strenner), Monatshefte fur Matematik 171 (2), (2013), 169-187. (pdf-file)


• Pointwise regularity of parameterized affine zipper fractal curves fractal curves, (with B. Barany, I. Kolossvary), Nonlinearity 31 (5), (2018), 1705-1733. (pdf-file)



Decomposition problems



• Decomposition of balls into finitely many pieces, (with M. Laczkovich), Mathematika 57 (1),(2011), 89-107. (pdf-file)


• Decomposition of balls in R^d, (with G. Somlai), Mathematika 62 (2), (2016), 378-405. (pdf-file)


• Decompositions of the positive real numbers into sets closed under addition and multiplication, (with G. Somlai, T. Terpai), in preparation



General metric spaces



• A generalization of the concept of distance based on the simplex inequality, (with J.-L. Marichal, B. Teheux), Contributions to Algebra and Geometry 59 (2), pp 247–266, (2018). (pdf-file)



Associative and bisymmetric functional equations



• A characterization of n-associative, monotone, idempotent functions on an interval that have neutral elements, (with G. Somlai), Semigroup Forum 96 (3), (2018), 438-451, doi.org/10.1007/s00233-017-9876-3. (pdf-file)


• Generalization of Czogała-Drewniak theorem for n-ary semigroups, (with G. Somlai), In: V. Torra, R. Mesiar, B. De Baets (eds.), Aggregation Functions in Theory and in Practice. Series: Advances in Intelligent Systems and Computing, Vol. 581. Springer, Berlin, 138-146 (2017).


• Associative idempotent nondecreasing functions are reducible, (with G. Somlai), published online at Semigroup Forum, https://doi.org/10.1007/s00233-018-9973-y. (pdf-file)


• Characterizations of quasitrivial symmetric nondecreasing associative operations, (with J. Devillet, J-L. Marichal), accepted at Semigroup Forum, (2018), (pdf-file)


• Visual characterization of associative quasitrivial nondecreasing functions on finite chains, submitted to Fuzzy Set and Systems. (pdf-file)


• Characterizations of biselective operations, (with J. Devillet), accepted at Acta Mathematica Hungarica, (2018), (pdf-file)