# Prof. Dr. Gát György

Beosztás: intézetigazgató, egyetemi tanár
Szobaszám: E114
Telefonszám: (42) 599-400/2187
E-mail: gatgy at nyf.hu
saját honlapja:
http://zeus.nyf.hu/~gatgy/

Prof. Dr. habil. Gát György szakmai önéletrajza

Kutatási területe: Analízis, Fourier sorok

### Publikációs lista:

•  Gát, G., One of the applications of the fast Fourier transform, Bulletins for Applied Mathematics 41 (1986), 102-105 ZBL 613.65146.
• Gát, G., On computing the generalized fast discrete Fourier transform, Bulletins for Applied Mathematics 45 (1987), 123-134 ZBL 636.65040.
• Gát, G., Vilenkin Fourier series and limit periodic arithmetical functions, Colloq Soc. J. Bolyai 58 Approx. Theory, Kecskemét, (Hungary) (1990), 315-332 ZBL 760.42013, MR 94g:42042.
• Gát, G., Orthonormal systems on Vilenkin groups, Acta Math. Hungar. 58(1-2)  (1991), 193-198 ZBL 753.11027, MR 93e:42039.
• Gát, G., On almost even arithmetical functions via orthonormal systems on Vilenkin groups, Acta Arith. 49(2) (1991), 105-123 ZBL 725.11049, MR 92j:11083.
• Gát, G., Investigation of certain operators with respect to the Vilenkin system, Acta Math. Hungar. 61(1-2) (1993), 131-149 ZBL 805.42019, MR 94d:42035.
• Gát, G., On the non-equivalence of Vilenkin-like systems, Acta Math. Acad. Paed. Nyiregyh. 13 (1993), 87-95 ZBL 913.42022.
• Gát, G., Investigation of some operators with respect to Vilenkin-like systems, Annales Univ. Sci. Budapestiensis 14 (1994), 61-70 ZBL 923.42018, MR 96a:42034.
• Gát, G., On a norm convergence theorem with respect to Vilenkin system in the Hardy spaces, Acta Acad. Paed. Agriensis Sectio Matematicae 22 (1994), 101-107 ZBL 882.42016.
• Gát, G., Pointwise convergence of Fejér means on compact totally disconnected groups, Acta Sci. Math. (Szeged) 60 (1995), 311-319 ZBL 835.43008, MR 96i:43007.
• Gát, G., Toledo, R., Lp-norm convergence of series in compact totally disconnected groups, Analysis Math. 22 (1996), 13-24 ZBL 856.42017, MR 97f:42043.
• Gát, G., Convergence and Summation With Respect to Vilenkin-like Systems in: Recent Developments in Abstract Harmonic Analysis with Applications in Signal Processing, Nauka, Belgrade and Elektronski fakultet, Nis, 1996, pp. 137-146.
• Gát, G., Pointwise convergence of double Walsh-Fejér means, Annales Univ. Sci. Budapestiensis, Sect. Comp. 16 (1996), 173-184 ZBL 891.42014, MR 99b:42033.
• Gát, G., On the almost everywhere convergence of Fejér means of functions on the group of 2-adic integers, Journal of Approx. Theory vol 90 (1) (1997), 88-96 ZBL 883.42021, MR 98m:42042.
• Gát, G., On the two-dimensional pointwise dyadic calculus, Journal of Approx. Theory 92 (2) (1998), 191-215 ZBL 897.42017, MR 99c:42049.
• Gát, G., On the lower bound of Sunouchi's operator with respect to the Vilenkin system, Analysis Math. 23 (1997), 259-272 ZBL 888.42017, MR 99f:42057.
• Gát, G., On the Fejér kernel functions with respect to the Walsh-Paley system, Acta Acad. Paed. Agriensis Sectio Matematicae 24 (1997), 105-110 ZBL 888.42015.
• Gát, G., On a theorem of type Hardy-Littlewood with respect to the Vilenkin-like systems, Acta Acad. Paed. Agriensis Sectio Matematicae 25 (1998), 83-89 ZBL 929.42018, MR 1 728 604.
• Gát, G., On (C; 1) summability of integrable functions with respect to the Walsh-Kaczmarz system, Studia Math. 130 (2) (1998), 135-148 ZBL 905.42-016, MR 99e:42043.
• Gát, G., On the Calderon-Zygmund decomposition lemma on the Walsh-Paley group, Acta Math. Acad. Paed. Nyiregyh. 14 (1998), 25-30 ZBL 908.42011, MR 1 712 506.
• Gát, G., Nagy, K., The fundamental theorem of two-paremeter pointwise derivate on Vilenkin groups, Analysis Math. 25 (1999), 33-55 ZBL 0932.42020, MR 1 678 505.
• Gát, G., Pointwise convergence of the Fejér means of functions on unbounded Vilenkin groups, Journal of Approx. Theory 101 (1) Nov (1999), 1-36 ZBL 0972.42019, MR 1 724 023.
• Gát, G., Toledo, R., Fourier coefficients and absolute convergence on compact totally disconnected groups, Math. Pannonica 10/2 (1999), 223-233 ZBL 0932.43010, MR 1 704 611.
• Gát, G., On the a.e. convergence of Fourier series on unbounded Vilenkin groups, Acta Math. Acad. Paed. Nyiregyh. 15 (1999), 27-34 ZBL 0980.42019, MR 1 706 915.
• Gát, G., On the divergence of the (C; 1) means of double Walsh-Fourier series, Proc. Amer. Math. Soc. 128 (2000), 1711-1720 ZBL 0976.42016, MR 1 657751
• Blahota, I., Gát, G., Pointwise convergence of double Vilenkin-Fejér means, Stud. Sci. Math. Hungar. 36 (2000), 49-63 ZBL 0973.42021, MR 2001h:42041
• Gát, G., Nagy, K., Investigation of the Sunouchi operator with respect to the Walsh-Kaczmarz system, Acta Math. Hungar. vol 89 (1-2) (2000), 93-101 ZBL 0973.42022, MR 2003e:42040
• Gát, G., On (C,1) summability for Vilenkin-like systems, Studia Math. 144 (2) (2001), 101-120 ZBL 0974.42020, MR 2001k:42033.
• Gát, G., On the Fejér kernel functions with respect to the Walsh-Kaczmarz system, Acta Math. Acad. Paed. Nyiregyh. 17(2) (2001), 121-126 MR 2002m:42030.
• Gát, G., Divergence of the (C, 1) means of d-dimensional Walsh-Fourier series, Analysis Math. 27 (2001), 157-171 ZBL 0996.40002, MR 2002j:42005
• Gát, G., Best approximation by Vilenkin-like systems, Acta Math. Acad. Paed. Nyiregyh. 17(3) (2001), 161-169 ZBL 0992.42011, MR 2002k:42057.
• Gát, G., Nagy, K., Cesaro summability of the character system of the p-series  field in the Kaczmarz rearrangement, Analysis Math 28 (2002), 1-36 MR 2003c:42011.
• Gát, G., On the divergence of the two-dimensional dyadic difference of dyadic integrals, Journal of Approximation Theory 116 (1) (2002), 1-27 ZBL 0999.42016, MR 1 909 010.
• Gát, G., On the Sunouchi operator with respect to the two-dimensional Walsh-Paley system, Function, Series, Operators - Alexits Memorial Conference, Budapest (Hungary), Colloq Soc. J. Bolyai 60 Approx. Theory, Budapest, (Hungary) (2002), 247-260.
• Gát, G., On term by term dyadic differentiability of Walsh-Kaczmarz series, Analysis in Theory and Applications (former title: Approximation Theory and Applications) 19 (1) (2003), 55-75.
• Gát, G., Cesaro means of integrable functions with respect to unbounded Vilenkin systems, Journal of Approximation Theory 124 (1) (2003), 25-43.
• Gát, G., On the L1 norm of the weighted maximal function of the Walsh- Kaczmarz-Dirichlet kernels, Acta Acad. Paed. Agriensis Sectio Matematicae 30 (2003), 55-66.
• 38. Gát, G., On the pointwise convergence of Cesaro means of two-variable functions with respect to unbounded Vilenkin systems, Journal of Approximation Theory 128 (1) (2004), 69-99.
• Gát, G., Convergence of Marcinkiewicz means of integrable functions with respect to two-dimensional Vilenkin systems, Georgian Math. Journ 10 (3) (2004), 467-478.
• Gát, G., Goginava, U., Uniform and L-convergence of logarithmic means of cubical partial sums of double Walsh-Fourier series, East Journal on Approx- imations 10 (4) (2004), 1-22.
• Gát, G., Convergence of Cesaro means of functions with respect to unbounded Vilenkin systems, Acta Math. Acad. Paed. Nyiregyh. 20 (2) (2004), 141-152.
• Gát, G., Goginava, U., Uniform and L-Convergence of logarithmic Means of d-dimensional Walsh-Fourier Series, Bull. Georg. Acad. Sci. 170 (2) (2004), 234-236.
• Gát, G., Goginava, U., Tkebuchava, G., Convergence in Measure of Logarithmic Means of -dimensional Walsh-Fourier series, Bull. Georg. Acad. Sci. 170 (3) (2004), 441-442.
• Gát, G., Goginava, U., Uniform and L-Convergence of Logarithmic Means of Cubical Partial Sums of d-dimensional Walsh-Fourier Series, Bull. Georg. Acad. Sci 171 (1) (2004), 234-236.
• Gát, G., Goginava, U., Uniform and L-convergence of logarithmic means of double Walsh-Fourier series, Georgian Math. Journ. 12 (1) (2005),  75-88.
• Gát, G., On the divergence of the Fejer means of integrable functions on two- dimensional Vilenkin groups, Acta Math. Hungar. 107 (1-2) (2005), 17-33.
• Gát, G., Divergence of Fejer means of Lipschitz functions on noncommuta- tive Vilenkin groups with respect to the character system, Acta Sci. Math. (Szeged), 71 (2005), 181-193.
• Gát, G., Properties of Fejer means of Fourier series with respect to unbounded Vilenkin systems, Rendiconti del Circolo Matematico di Palermo, Serie II, Suppl. 76 (2005), 355-373.
• Gát, G., Goginava, U., Tkebuchava, G., Convergence in measure of logarithmic means of double Walsh-Fourier series, Georgian Math. Journal, 12 (2005), No. 4, 607--618.
• Gát, G., Goginava, U., Tkebuchava, G., Convergence of logarithmic means of multiple Walsh-Fourier series, Analysis in Theory and Applications (former title: Approximation Theory and Applications), 21 (4)(2005), 326-338.
• Gát, G., Goginava, U., Uniform and L-convergence of logarithmic means of Walsh-Fourier series, Acta Mathematica Sinica (English Series), 22 (2006), No 2, 497-506.
• Gát, G., Fejér means of functions on noncommutative Vilenkin groups with respect to the character system, Analysis Math., 32 (2006), 25-48.
• Gát, G., Goginava, U., Tkebuchava, G.,   Convergence in measure of logarithmic means of quadratical partial sums of double Walsh-Fourier series, Journal of Math. Anal. and Appl. 323 (2006), 535-549.
• Gát, G., Goginava, U., Nagy, K., On (Hpq,Lpq)-type inequality of maximal operator of Marcinkiewicz-Fej´er means of double Fourier series with respect to the Kaczmarz system, Math. Ineq. and Applications, 9 (3) (2006), 473-483.
• Gát, G., On convergence properties of logarithmic means of Walsh-Fourier series, CFT Constructive Function Theory, Varna, julius 1-7, 2005 (B. Bojanov, Ed.) Marin Drinov Academic Publishing House, Sofia, 2006, 113-120.
• Gát, G., Goginava, U., Almost Everywhere Convergence of (C, a)-Means of Quadratical Partial sums of double Vilenkin-Fourier Series, Georgian Math. J., 13 (3) (2006), 447-462.
• Gát, G., Goginava, U., Maximal convergence space of a subsequence of the logarithmic means of rectangular partial sums of double Walsh-Fourier series, Real Analysis Exchange, 31 (2) (2006), 447-464.
• Blahota, I., Gát, G., Goginava, U., Maximal operators of Fejer means of double Vilenkin-Fourier series, Colloquium Mathematicum, 107 (2) (2007), 287-296.
• Gá́t, G., Goginava, U., Almost everywhere Convergence of a Subsequence of the Logarithmic means of quadratical partial sums of Double Walsh-Fourier Series, Publ. Math. Debrecen 71 (1-2) (2007), 173-184.
• Gá́t, G., Almost everywhere convergence of Cesáro means of Fourier series on the group of 2-adic integers Acta Math Hungar. 116 (3) (2007), 209-221.
• Gá́t, G., Pointwise convergence of cone-like restricted two-dimensional (C, 1) means of trigonometric Fourier series, Journal of Approximation Theory 149 (1) (2007), 74-102.
• Gá́t, G., Almost everywhere convergence of Fejé́r means of L1 functions on rarely unbounded Vilenkin groups, Acta Math. Sinica (English Series) 23 (12) (2007), 2269-2294.
• Blahota, I., Gá́t, G., Norm summability of Nö̈rlund logarithmic means on un-bounded Vilenkin groups, Analysis in Theory and Applications 24 (1) (2008), 1-17.
• Gá́t, G., Convergence and divergence of Fejé́r means of Fourier series on one and two-dimensional Walsh and Vilenkin groups, Facta Universitatis (Series: Electronics and Energetics) published by the University of Nis, YU ISSN  0353-3670 http://factaee.elfak.ni.ac.yu/. 21(3) (2008), 291-307.
• Gá́t, G., Nagy, K., Almost everywhere convergence of a subsequence of the logarithmic means of Vilenkin Fourier series, Facta Universitatis (Series: Electronics and Energetics) published by the University of Nis, YU ISSN 0353-3670 http://factaee.elfak.ni.ac.yu/. 21 (3) (2008), 275-289.
• Blahota, I., G át, G., Almost everywhere convergence of Marcinkiewicz means of Fourier series on the group of 2-adic integers, Studia Math. 191 (3) (2009), 215-222.
• Gá́t, G., Toledo, R., On the convergence in L^1 -norm of Cesaro means with respect to representative product systems, Acta Math. Hungar. 123 (1-2) (2009), 103-120.
• Gá́t, G., Goginava, U., On the divergence of Nö̈rlund logarithmic means of Walsh-Fourier series, Acta Math. Sinica (English series) 25 (6) (2009), 903-916.
• Gát, Gy., Goginava, U., Nagy, K., On Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system, Studia Sci. Math. Hung. 46 (3), (2009) 399-421.
• Gát, Gy., Nagy, K.,  On the $(C,\alpha)$-means of  quadratic partial sums of double Walsh-Kaczmarz-Fourier series, Georgian Math. J. 16 (3), (2009) 489-506.
• Gát, G., On almost everywhere convergence of Fourier series on unbounded Vilenkin groups, Publ. Math. Debrecen 75 1-2 (2009), 85-94.
• Gát, G., Goginava, U., The weak type inequality for the maximal operator of the (C; a) -means of the Fourier series with respect to the Walsh-Kaczmarz system, Acta Math. Hungar. 125 (1-2) (2009), 65-83.
• Gát, G., Almost everywhere convergence of Fejér and logarithmic means of subsequences of partial sums of the Walsh-Fourier series of integrable functions, J. of Approx. Theory 162 (2010), 687-708.

• Gát, G., Nagy, K., Pointwise convergence of cone-like restricted twodimensional Fejér means of Walsh-Fourier series, Acta Mathematica Sinica (English series) 1 (2010), 2295-2304.

• Gát, G., Some convergence and divergence results with respect to summation of Fourier series on one and two-dimensional unbounded Vilenkin groups, Annales Univ. Sci. Budapestiensis 33 (2010), 157-173.

• Gát, G., Nagy, K., On the logarithmic summability of Fourier series, Georgian Math. Journal 18 (2) (2011), 237-248.

• Gát, G., Reconstruction of functions via Walsh-Fourier cofficients, R. Moreno- Daz et al. (Eds.): EUROCAST 2011, Part II, LNCS 6928, Springer, Heidelberg (2011), 351-358.

• Gát, G., On almost everywhere convergence and divergence of Marcinkiewicz like means of integrable functions with respect to the two-dimensional Walsh system, Journal of Approx. Theory 164 (2012), 145-161.

• Gát, G., Almost everywhere convergence of sequences of two-dimensional Walsh-Fejér means of integrable functions,Acta Math. Hungar., 134 (4) (2012), 589-601.

• Gát, G., Convergence of sequences of two-dimensional Fejér means of trigonometric Fourier series of integrable functions, Journal of Math. Anal. and Appl., 390 (2012), 573-581.