Research publications of Mihalis Kolountzakis

Approximately in reverse chronological order. All files are in PDF and the oldest ones are in Postscript as well.

1. Sigrid Grepstad and M.N.K, Bounded common fundamental domains for two lattices,
   submitted
   

2. M.N.K and Chun-Kit Lai, Non-spectrality of some piecewise smooth curves and unions of line segments,
   submitted
   

3. M.N.K, Nir Lev and Máté Matolcsi, Geometric implications of weak tiling,
   submitted
   

4. M.N.K and Sha Wu, Spectrality of a measure consisting of two line segments,
   submitted
   

5. M.N.K, Nir Lev and Máté Matolcsi, Maximality and completeness of orthogonal exponentials on the cube,
   Expositiones Math. to appear
   

6. M.N.K and Emmanuil Spyridakis, Exponential polynomials and identification of polygonal regions from Fourier samples,
   submitted
   

7. M.N.K, Orthogonal Fourier Analysis on Domains,
   Expositiones Math. to appear
   

8. M.N.K and Emmanuil Spyridakis, Curves in the Fourier zeros of polytopal regions and the Pompeiu problem,
   Analysis Mathematica, to appear
   

9. Rachel Greenfeld and M.N.K, Tiling, spectrality and aperiodicity of connected sets,
   Israel J. Math., to appear
   

10. M.N.K, Sets of full measure avoiding Cantor sets,
    Bull. Hellenic Math. Soc. 67 (2023), 1-11.
    

11. M.N.K, Nir Lev and Máté Matolcsi, Spectral sets and weak tiling,
    Sampling Theory, Signal Processing, and Data Analysis, Volume 21, article number 31, (2023).
    

12. M.N.K and Effie Papageorgiou, Large sets containing no copies of a given infinite sequence,
    Analysis and PDE, 18:1 (2025), 93–108.
    

13. M.N.K, Simultaneous tiling,
    D. Gatzouras memorial volume, Univ. of Athens, 2022,
    

14. Benedikt Diederichs, M.N.K and Effie Papageorgiou, How many Fourier coefficients are needed,
    Monatshefte für Mathematik volume 200, pages23–42 (2023)
    

15. M.N.K and Effie Papageorgiou, Functions tiling with several lattices,
    J. Fourier Anal. Appl. 28, 68 (2022).
    

16. M.N.K and Nir Lev, Tiling by translates of a function: results and open problems,
    Discrete Analysis, 2021:12, 24 pp.
    

17. M.N.K, Deciding multiple tiling by polygons in polynomial time,
    Periodica Math. Hungarica, 83, 32–38 (2021).
    

18. Alex Iosevich, M.N.K, Yurii Lyubarskii, Azita Mayeli and Jonathan Pakianathan, On Gabor orthonormal bases over finite prime fields,
    Bulletin of the London Math. Soc. 53: 380-391 (2021).
    

19. M.N.K and Yang Wang, The structure of multiplicative tilings of the real line,
    J. Fourier Anal. Appl., 25 (2019), 3, 1248–1265.
    

20. Elona Agora, Jorge Antezana and M.N.K, Tiling functions and Gabor orthonormal bases,
    Appl. Comp. Harm. Anal., 48 (2020), 1, 96–122.
    

21. M.N.K, Máté Matolcsi and Mihály Weiner, An application of positive definite functions to the problem of MUBs,
    Proc. AMS, 146 (2018) 3, 1143-–1150.
    

22. Romanos Malikiosis and M.N.K, Fuglede's conjecture on cyclic groups of order $p^nq$,
    Discrete Analysis, 2017:12, 16 pp.
    

23. M.N.K, Packing near the tiling density and exponential bases for product domains,
    Bull. Hellenic Math. Soc. 60 (2016), 97-109.
    

24. Michael Papadimitrakis and M.N.K, Measurable Steinhaus sets do not exist for finite sets or the integers in the plane,
    Bulletin London Math. Soc., 49, 5 (2017), 798–805.
    

25. Agelos Georgakopoulos and M.N.K, On particles in equilibrium on the real line,
    Proc. Amer. Math. Soc. 145 (2017), 3501-3511.
    

26. Elona Agora, Sigrid Grepstad and M.N.K, Spectra for cubes in products of finite cyclic groups,
    Proc. AMS, 146 (2018), 6, 2417-–2423.
    

27. M.N.K, Discrepancy of line segments for general lattice checkerboards,
    Anal. Math. 42 (2016), 1, 31–41.
    

28. M.N.K and Nir Lev, On non-periodic tilings of the real line by a function,
    Int. Math. Res. Not. 15 (2016), 4588–4601.
    

29. M.N.K, Fourier pairs of discrete support with little structure,
    J. Fourier Anal. Appl. 22 (2016), 1, 1-5.
    

30. M.N.K, Multiple lattice tiles and Riesz bases of exponentials,
    Proc. Amer. Math. Soc. 143 (2015), 741-747
    

31. Nick Gravin, M.N.K, Sinai Robins and Dmitry Shiryaev, Structure results for multiple tilings in 3D,
    Discrete & Computational Geometry, December 2013, Volume 50, Issue 4, pp 1033-1050.
    

32. M.N.K and Yannis Parissis, Circle discrepancy for checkerboard measures,
    Illinois J. Math., Volume 56, Number 4 (2012), 1297-1312.
    

33. Alex Iosevich and M.N.K, Size of orthogonal sets of exponentials for the disk,
    Rev. Mat. Iberoamericana, 29 (2013), 739–747.
    

34. Alex Iosevich and M.N.K, Periodicity of the spectrum in dimension one,
    Analysis & PDE 6-4 (2013), 819–827.
    

35. M.N.K, Periodicity of the spectrum of a finite union of intervals,
    J. Fourier Anal. Appl., 18 (2012), 1, 21–26.
    

36. M.N.K, Gary L. Miller, R. Peng and Charalambos Tsourakakis, Efficient Triangle Counting in Large Graphs via Degree-Based Vertex Partitioning,
    in Algorithms and Models for the Web-Graph, Lecture Notes in Comp. Sci. 6516 (2010), 15–24, Springer, Berlin, and in
    Internet Mathematics, 8.1-2 (2012), 161-185.
    

37. M.N.K and Máté Matolcsi, Tilings by translation,
    La Gaceta de la Real Sociedad Espanola, 13 (2010), 4.
    

38. Charalambos Tsourakakis, M.N.K and Gary L. Miller, Triangle Sparsifiers,
    J. of Graph Algorithms and Appl., J. Graph Algorithms Appl. 15.6 (2011), 703-726.
    

39. Alex Iosevich and M.N.K, The discrepancy of a needle on a checkerboard, II,
    Uniform Distribution Theory, 5 (2010), 2, 1–13.
    

40. M.N.K and Máté Matolcsi, Algorithms for translational tiling,
    J. Math. and Music, 3 (2009), 2, 85–97.
    ,

41. M.N.K, Coefficients of squares of Newman polynomials,
    will not be published.
    ,

42. M.N.K, The discrepancy of a needle on a checkerboard,
    Online J. Analytic Combinatorics, 3 (2008), #7.
    ,

43. Alex Iosevich, M.N.K and Máté Matolcsi, Covering the plane by rotations of a lattice arrangement of disks,
    in Complex and Harmonic Analysis, Proceedings of the International Conference, Thessaloniki, May 25 -27 2006, Destech Publications Inc..
    ,

44. M.N.K, Richard Lipton, Vangelis Markakis, Aranyak Mehta and Nisheeth Vishnoi, On the Fourier spectrum of symmetric boolean functions,
    Combinatorica, 29 (2009), 3, 363–387.
    ,

45. Tamás Keleti and M.N.K, On the determination of sets by their triple correlation in finite cyclic groups,
    Online J. Analytic Combinatorics, 1 (2006), #4.
    ,

46. M.N.K, Vangelis Markakis and Aranyak Mehta, Learning symmetric $k$-juntas in time $n^{o(k)}$,
    Proceedings of the conference Interface entre l'analyse harmonique et la theorie des nombres, CIRM, Luminy, October 2005, to appear
    ,

47. M.N.K and Máté Matolcsi, Complex Hadamard matrices and the Spectral Set Conjecture,
    Collectanea Mathematica, Vol Extra (2006), 281-291.
    ,

48. M.N.K Filling a box with translates of two bricks,
    Electr. J. Combin., 11 (2004), N16.
    ,

49. M.N.K and Máté Matolcsi, Tiles with no spectra,
    Forum Math. 18 (2006), 3, 519–528.
    ,

50. M.N.K and Szilard Gy. Revész, Turán's extremal problem for positive definite functions on groups,
    J. London Math. Soc. (2) 74 (2006), 2, 475–496.
    ,

51. Alex Iosevich and M.N.K, A Weyl type formula for Fourier spectra and frames,
    Proc. AMS, 134 (2006), 11, 3267–3274.
    ,

52. Phillipe Jaming and M.N.K, Reconstruction of functions from their triple correlations,
    New York Journal of Mathematics 9 (2003), 149-164.
    ,

53. (Survey) M.N.K, The study of translational tiling with Fourier Analysis,
    Fourier Analysis and Convexity, 131–187, Appl. Numer. Harmon. Anal., Birkhäuser Boston, Boston, MA, 2004.
    ,

54. M.N.K, Distance sets corresponding to convex bodies,
    Geom. and Funct. Anal., 14 (2004), 4, 734-744.
    ,

55. M.N.K and Szilard Gy. Revész, On pointwise estimates of positive definite functions with given support,
    Canadian J. Math. 58 (2006), 2, 401–418.
    ,

56. M.N.K, Translational tilings of the integers with long periods,
    Electr. J. Combinatorics 10 (2003), 1, R22.
    ,

57. M.N.K and Szilard Gy. Revész, On a problem of Turán about positive definite functions,
    Proc. AMS, 131 (2003), 3423-3430.
    ,

58. M.N.K and Izabella Łaba, Tiling and spectral properties of near-cubic domains,
    Studia Math., 160(2004), 287-299.
    ,

59. M.N.K and Michael Papadimitrakis, A class of non-convex polytopes that admit no orthonormal basis of exponentials,
    Illinois J. Math., 46 (2002), 4, 1227-1232.
    ,

60. M.N.K and Michael Papadimitrakis, The Steinhaus tiling problem and the range of certain quadratic forms,
    Illinois J. Math. 46 (2002), 3, 947-951.
    ,

61. M.N.K , A remark on perturbations of sine and cosine sums,
    preprint.
    ,

62. M.N.K, Packing, tiling, orthogonality and completeness,
    Bull. London Math. Soc. 32 (2000), 5, 589-599.
    ,

63. M.N.K, Non-symmetric convex domains have no basis for exponentials,
    Illinois J. Math. 44 (2000), 3, 542-550.
    ,

64. M.N.K, On the structure of multiple translational tilings by polygonal regions,
    Discr. Comp. Geom. 23 (2000), 4, 537-553.
    ,

65. M.N.K, On the uniform distribution in residue classes of dense sets of integers with distinct sums,
    J. Number Th. 76 (1999), 147-153.
    ,

66. M.N.K and Thomas Wolff, On the Steinhaus tiling problem,
    Mathematika, 46 (1999), 2, 253-280.
    ,

67. M.N.K, Lattice tilings by cubes: whole, notched and extended,
    Electr. J. Combinatorics 5 (1998), 1, R14.
    ,

68. Lydia Kavraki, M.N.K and Jean-Claude Latombe, Analysis of Probabilistic Roadmaps for Path Planning,
    IEEE Transactions on Robotics and Automation 14 (1998), 1, 166-171. Also in Proc. IEEE Conf. Robotics and Automation, Minneapolis, 1996, 3020-3025.
    ,

69. M.N.K, Multi-lattice tiles,
    Intern. Math. Research Notices, 1997, 19, 937-952.
    ,

70. M.N.K, Lattice-tiling properties of integral self-affine functions,
    Appl. Math. Letters, 10 (1997), 5, 1-4.
    ,

71. M.N.K, Infinite Patterns That Can Be Avoided by Measure,
    Bull. London Math. Soc. 29 (1997), 4, 415-424.
    ,

72. (Survey) M.N.K, Some Applications of Probability to Additive Number Theory and Harmonic Analysis,
    in Number Theory: New York Seminar 1991-1995, Springer Verlag (1996).
    ,

73. M.N.K, On the Additive Complements of the Primes and Sets of Similar Growth,
    Acta Arith, 77 (1996), 1, 1-8.
    ,

74. M.N.K, A New Estimate for a Problem of Steinhaus,
    Intern. Math. Res. Notices, 1996, 11, 547-555.
    ,

75. M.N.K, A Problem of Steinhaus: Can All Placements of a Planar Set Contain Exactly One Lattice Point?
    Analytic Number Theory: Proceedings of a conference in honor of H. Halberstam, Birkhäuser, 1996.
    ,

76. M.N.K and Jeff Lagarias, Tilings of the Line by Translates of a Function,
    Duke Math. J. 82 (1996), 3, 653-678.
    ,

77. M.N.K, The Density of $B_h[g]$ Sets and the Minimum of Dense Cosine Sums,
    J. Number Theory 56 (1996), 1, 4-11.
    ,

78. Noga Alon and M.N.K, On a Problem of Erdős and Turán and Some Related Results,
    J. Number Theory 55 (1995), 1, 82-93.
    ,

79. Lydia Kavraki and M.N.K, Partitioning a Planar Assembly Into Two Connected Parts is NP-Complete,
    Inf. Proc. Letters 55 (1995), 159-165.
    ,

80. M.N.K, Selection of a Large Sum-Free Subset in Polynomial Time,
    Inf. Proc. Letters 49 (1994), 255-256.
    ,

81. M.N.K, An Effective Additive Basis for the Integers,
    Discr. Math. 145 (1995), 307-313. Also in Proc. Symposium On Discrete Algorithms (SODA) 1994.
    ,

82. M.N.K, A Construction Related to the Cosine Problem,
    Proc. Amer. Math. Soc. 122 (1994), vol. 4, 1115-1119.
    ,

83. M.N.K, On Nonnegative Cosine Polynomials with Nonnegative, Integral Coefficients,
    Proc. Amer. Math. Soc. 120 (1994), vol. 1, 157-163.
    ,

84. M.N.K and Kyriakos Kutulakos, Fast Computation of the Euclidean Distance Map for Binary Images,
    Inf. Proc. Letters 43 (1992), 181-184.
    ,

85. M.N.K and Stelios C. Orphanoudakis, Computing Line Sums on a Mesh Connected Computer,
    Technical Report, Institute of Computer Science, Foundation of Research and Technology, Hellas, Greece, 1988.
    

86. M.N.K, Probabilistic and constructive methods in harmonic analysis and additive number theory,
    PhD Thesis, Stanford University, June 1994.
    ,

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