Christoph Thiele

Professor

See MathSciNet . See Math Genealogy . See Arxiv . See Google Scholar .

Sected preprints and papers:

  1. (with F. van Doorn, P. Durcik, J. Roos, and L Slavikova) "A blueprint for the formalization of norm-variation of multiple ergodic averages for commuting transformations " arXiv:2608.27321

  2. (with L. Becker, A. Jamneshan) "Quantitative Polynomial Wiener-Wintner Theorems " arXiv:2601.03999

  3. (with M. Alexis, L. Becker, D. Oliveira e Silva) "An SU(2n)-valued nonlinear Fourier transform " arXiv:2601.03987

  4. (with L. Becker, F. van Doorn, A. Jamneshan, R. Srivastava) "Carleson operators on doubling metric measure spaces " arXiv:2508.05563

  5. (with M. Alexis, G. Mnatsakanyan) "One sided orthogonal polynomials and a pointwise convergence result for SU(2)-valued nonlinear Fourier series" arXiv:2507.05124

  6. (with M. Alexis, L. Lin, G. Mnatsakanyan, J. Wang) "Infinite quantum signal processing for arbitrary Szego functions " Selected for a presentation in 28th Annual Quantum Information Processing Conference 2025. Comm. Pure Appl. Math. 79 (2026), no. 1, 123–174. arXiv:2407.05634

  7. (with L. Becker, M. Inés de Frutos-Fernández, L. Diedering, F. van Doorn, S. Gouëzel, A. Jamneshan, E. Karunus, E. van de Meent, P. Monticone, J. Mulder-Sohn, J. Portegies, J. Roos, M. Rothgang, R. Srivastava, J. Sundstrom, J. Tan) "A blueprint for the formalization of Carleson's theorem on convergence of Fourier series" arXiv:2405.06423v2

  8. (with M. Fraccaroli and O. Saari) "Uniform bounds for bilinear symbols with linear K-quasiconformally embedded singularity " Anal. PDE 18 (2025), no. 9, 2293–2323. arXiv:2402.11661

  9. (with M. Alexis and G. Mnatsakanyan) "Quantum signal processing and nonlinear Fourier analysis" Rev. Mat. Complutense 37 (2024) no 3. 655-694 arXiv:2310.12683

  10. (with P. Durcik and L. Slavikova) "Norm-variation of triple ergodic averages for commuting transformations" Anal. PDE 19 (2026), no. 3, 539–586 arXiv:2307.07372

  11. (with M. Fraccaroli and O. Saari) "Phase space localizing operators" arXiv:2210.16164

  12. (with G. Negro and D. Oliveira e Silva) "When does exp(-tau) maximize Fourier extension for a conic section?" Harmonic analysis and convexity, 391–426. Adv. Anal. Geom., 9 arXiv:2209.03916

  13. (with P. Durcik and L Slavikova) "Local bounds for singular Brascamp Lieb forms with cubical structure." Math. Z. 302 (2022), no. 4, 2375–2405. arXiv:2112.15101

  14. (with O. Saari) "Paraproducts for bilinear multipliers associated with convex sets." Math. Z. 302 (2022), no. 4, 2375–2405. arXiv:2102.10305

  15. (with J. Barker, P. Zorin-Kranich) "Band-limited maximizers for a Fourier extension inequality on the circle, II." Exp. Math. 32 (2023), no. 2, 280–293. arXiv:2002.05118

  16. (with P. Durcik) "Singular Brascamp-Lieb: a survey." Springer INdAM Ser., 45 Springer, Cham, 2021, 321–349. arXiv:1904.08844:

  17. (with P. Durcik) "Singular Brascamp-Lieb inequalities ." Bull. Lond. Math. Soc. 52 (2020), no. 2, 283–298. arXiv:1809.08688:

  18. (with D. Oliveira e Silva, P. Zorin-Kranich) "Band-limited maximizers for a Fourier extension inequality on the circle." Exp. Math. 31 (2022), no. 1, 192–198. arXiv:1806.06605:

  19. (with F. DiPlinio, S. Guo, P. Zorin-Kranich) "Square functions for bi-Lipschitz maps and directional operators." J. Fourier Anal. Appl. 25 (2019), no. 1, 167–183. arXiv:1706.07111:

  20. (with O. Saari) "Lipschitz linearization of the maximal hyperbolic cross multiplier ." Journal of Fourier Analysis and Applications volume 25, pages 167–183(2019) arXiv:1701.05093:

  21. "On the first chapter." arXiv:1706.08905:

  22. (with P. Durcik, V. Kovac) "Power-type cancellation for the simplex Hilbert transform." J. Anal. Math. 139 (2019), no. 1, 67–82. arXiv1608.00156:

  23. (with Y. Do, C. Muscalu) "Variational estimates for the bilinear iterated Fourier integral." J. Funct. Anal. 272 (2017), no. 5, 2176–2233. arXiv:1605.00574

  24. (with S. Guo) "Hilbert transforms along Lipschitz direction fields: A lacunary model." Mathematika 63 (2017), no. 2, 351–363. arXiv:1603.03317

  25. (with P. Durcik, V. Kovac, K. Skreb) "Norm-variation of ergodic averages with respect to two commuting transformations." Ergodic Theory Dynam. Systems 39 (2019), no. 3, 658–688. arXiv:1603.00631

  26. (with P. Gressman, D. He, V. Kovac, B.Street, P.-L. Yung) "On a trilinear singular integral form with determinantal kernel." Proc. Amer. Math. Soc., Volume 144, Number 8, August 2016, Pages 3465–3477 arXiv:1510.01069

  27. (with E. Carneiro, D. Foschi, D. Oliveira e Silva) "A sharp trilinear inequality related to Fourier restriction on the circle." Rev. Mat. Iberoam. 33 (2017), no. 4, 1463–1486. arXiv:1509.06674

  28. (with D. Oliveira e Silva) "Estimates for certain integrals of products of six Bessel functions ." Rev. Mat. Iberoam. 33 (2017), no. 4, 1423–1462. arXiv:1509.06309

  29. (with M. Mirek) "A local Tb theorem for perfect multilinear CZ operators." Proc. Lond. Math. Soc. (3) 114 (2017), no. 1, 35–59. arxiv 1506.01264

  30. (with V. Kovac and P. Zorin-Kranich) "Dyadic triangular Hilbert transform of two general and one not too general function." Forum Math. Sigma 3 (2015), e25, 27 pp. arxiv 1506.00861

  31. (with S. Treil and A. Volberg ) "Beyond the scope of doubling measures: weighted martingale transforms via outer measures" Adv. Math. 285 (2015), 1155-1188. arxiv 1411.5345 An older shorter version is available here ,

  32. (with F. Di Plinio ) "Endpoint bounds for the bilinear Hilbert transform" Trans. Amer. Math. Soc. 368 (2016), no. 6, 3931-3972. arxiv 1403.5978 ,

  33. (with Y. Do ) "Lp theory for outer measures and two themes of Lennart Carleson united" Bulletin AMS (N.S.) 52 (2015) 249-296 arxiv 1309.0945 ,

  34. (with V. Kovac ) "A T(1) theorem for entangled multilinear dyadic Calderón-Zygmund operators " Illinois J. of Math. 57 (2013) no. 3. 775-799 arxiv 1305.4752 ,

  35. (with T. Tao ) "Nonlinear Fourier analysis" (from Park City Lecture Notes 2003) arxiv 1201.5129 ,

  36. (with M. Bateman ) "Lp estimates for the Hilbert transforms along a one variable vector field" Analysis and PDE 6 (2013) no 7. 1577-1600 arxiv 1109.6396 ,

  37. (with M. Reguera ) "The Hilbert transform does not map L1(Mw) to L{1,infty}(w)" arxiv:1011.1767 ,

    Math. Res. Lett. 19 (2012), no. 1, 1--7.

  38. (with Y. Do, C. Muscalu ) "Variational estimates for paraproducts" Rev. Mat. Iberoamericana 28 (2012), no. 3, 857--878. arxiv:1009.5187 ,

  39. (with R. Oberlin ) "New uniform bounds for a Walsh model of the bilinear Hilbert transform." arxiv:1004.4019 , Indiana Univ. Math. J. 60 (2011), no. 5, 1693–1712.

  40. (with F. Nazarov, R. Oberlin, ) "A Calderon Zygmund decomposition for multiple frequencies and an application to an extension of a lemma of Bourgain." Math. Res. Lett. 17 (2010), no. 3, 529--545. arxiv:0912.3010 ,

  41. (with R. Oberlin, A. Seeger, T. Tao, J. Wright ) "A variation norm Carleson theorem" J. Eur. Math. Soc. (JEMS) 14 (2012), no. 2, 421--464 arxiv:0910.1555 ,

  42. (with C. Demeter, M. Pramanik) "Multilinear singular operators with fractional rank" Pacific J. of Mathematics 246 (2010) no. 2, 293--324 arxiv:0904.1253 ,

  43. (with C. Demeter) "On the two dimensional Bilinear Hilbert Transform" Amer. J. Math. 132 (2010), no. 1, 201--256. arxiv:0803.1268 ,

  44. (with C. Demeter, M. Lacey, T. Tao ) "The Walsh model for M2* Carleson" Rev. Mat. Iberoam. 24 (2008), no. 3, 721--744. arxiv:0712.1295 ,

  45. (with C. Muscalu, T. Tao) "Multilinear operators associated to simplexes of arbitrary length" arxiv:0712.2420 , Advances in analysis: the legacy of Elias M. Stein, 346–401, Princeton Math. Ser., 50, Princeton Univ. Press, Princeton, NJ, 2014.

  46. (with A. Benyi, C. Demeter, A. Nahmod, R. Torres, F. Villarroya) "Modulation invariant bilinear T(1) theorem" J. Anal. Math. 109 (2009), 279--352. arxiv:0710.0973 ,

  47. "Applications of Time-frequency analysis in Ergodic Theory" Survey article for Oberwolfach meeting 2008 pdf file ,

  48. (with C. Demeter, M. Lacey, T. Tao) "Breaking the duality in the return times theorem." Duke Math. J. 143 (2008), no. 2, 281--355. arxiv.org/abs/math/0510581

  49. (with C. Demeter, T. Tao) "Maximal multilinear operators" Trans. Amer. Math. Soc. 360 (2008), no. 9, 4989--5042. arxiv.org/abs/math/0510581

  50. (with D. Müller) "Wave equation and multiplier estimates on ax+b groups." Studia Math. 179 (2007), no. 2, 117--148. arxiv.org/abs/math/0403476

  51. (with C. Muscalu, J. Pipher and T. Tao) "Multi-parameter paraproducts" Rev. Mat. Iberoam. 22 (2006), no. 3, 963--976. arxiv.org/abs/math/0411607

  52. (with C. Muscalu and T. Tao) "The bi-Carleson operator" Geom. Funct. Anal. 16 (2006), no. 1, 230--277. math.CA/0409406

  53. "Wave Packet Analysis" CBMS Regional Conference Series in Mathematics, 105. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2006. vi+86 pp. ISBN: 0-8218-3661-7

  54. (with M. Christ, X. Li and T. Tao) "On multilinear oscillatory integrals, nonsingular and singular." . Duke Math. J. 130 (2005), no. 2, 321--351. math.CA/0311039

  55. (with C. Muscalu J. Pipher, and T. Tao) "Bi-parameter paraproducts" Acta Math. 193 (2004), no. 2, 269--296. math.CA/0310367

  56. (with C. Muscalu and T. Tao) "Lp estimates for the biest. II. The Fourier case." Math. Ann. 329 (2004), no. 3, 427--461. math.CA/0205139

  57. (with C. Muscalu and T. Tao) "A Carleson type theorem for a Cantor group model of the scattering transform" Nonlinearity 16 (2003), no. 1, 219--246. math.CA/0205139

  58. (with P. Auscher, S. Hofmann, C. Muscalu, T. Tao) "Carleson measures, trees, extrapolation, and T(b) theorems" Publ. Mat. 46 (2002), no. 2, 257--325. math.CA/0108138

  59. "Singular integrals meet modulation invariance" Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), 721--732, Higher Ed. Press, Beijing, 2002. pdf file , dvi file ,

  60. (with C. Muscalu and T. Tao) " A discrete model for the bi-Carleson operator. "
    Geom. Funct. Anal. 12 (2002), no. 6, 1324--1364. math.CA/0201060

  61. (with C. Muscalu and T. Tao) " Lp estimates for the biest I. The Walsh case"
    Math. Ann. 329 (2004), no. 3, 401--426. math.CA/0102083

  62. (with C. Muscalu and T. Tao) " Lp estimates for the biest II. The Fourier case"
    Math. Ann. 329 (2004), no. 3, 427--461. math.CA/0102084

  63. (with C. Muscalu and T. Tao) "A counterexample to a multilinear endpoint question of Christ and Kiselev" ,
    Math. Res. Lett. 10 (2003), no. 2-3, 237--246. math.CA/0108156
  64. (with C. Muscalu and T. Tao) "Uniform estimates on multi-linear operators with modulation symmetry. Dedicated to the memory of Tom Wolff." ,
    J. Anal. Math. 88 (2002), 255--309. math.CA/0107059
  65. (with C. Muscalu and T. Tao) "Uniform estimates on paraproducts. Dedicated to the memory of Thomas H. Wolff." ,
    J. Anal. Math. 87 (2002), 369--384. math.CA/0106092
  66. "Multilinear singular integrals" ,
    survey article El Escorial 2000, preprint Mar 2001, pdf file , dvi file ,

  67. "A uniform estimate",
    Ann. of Math. (2) 156 (2002), no. 2, 519--563.

  68. "A uniform estimate for the quartile operator",
    Rev. Mat. Iberoamericana 18 (2002), no. 1, 115--134.

  69. (with C. Muscalu and T. Tao) "Multi-linear operators given by singular multipliers",
    J. Amer. Math. Soc. 15 (2002), no. 2, 469--496 (electronic). math.CA/9910039
  70. (with D. Mueller), "Normal forms of involutive complex Hamiltonian matrices under the real symplectic group."
    J. Reine Angew. Math. 513 (1999), 97--114.

  71. (with M. Lacey) "A proof of boundedness of the Carleson operator"
    Revised June 2000 from previous "Convergence of Fourier series"    ,
    Math.Res. Lett 7 (2000) 361-370

  72. "On the Bilinear Hilbert Transform",
    Habilitationsschrift, Universität Kiel, 1998 ps file

  73. "Time-Frequency Analysis in the Discrete Phase Plane",
    PhD thesis Yale 1995, ps file


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