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Neal Bez

2015.01.06 更新

  • 氏名Neal Bez
  • 職名准教授(Associate Professor)
  • 所属理工学研究科数理電子情報部門(Department of Mathematics)
  • 卒業研究

研究分野

  • Harmonic Analysis, Partial Differential Equations, Geometric Analysis, Geometric Computation

    調和解析、偏微分方程式、幾何解析、計算幾何

研究テーマ

My primary research interests lie in partial differential equations, harmonic analysis and geometric analysis. For example, Strichartz estimates for the solution of various evolution equations, including dispersive equations and transport equations. For dispersive equations, such estimates are directly related to questions in the context of the Stein restriction conjecture, which is a central problem in euclidean harmonic analysis, and enjoys further connections to problems in geometric analysis, such as the Kakeya conjecture and, via the multilinear perspective, to various generalisations of the Brascamp-Lieb inequality. Recently, I have been particularly interested in establishing optimal versions of such estimates, seeking sharp constants and information about the nature of maximising input functions when they exist, for example, via heat flow methods. In a different direction, I am also interested in geometric computation, including the analysis of Bézier curves and subdivision of curves and surfaces.

私の主な研究分野は、偏微分方程式、調和解析と幾何解析です。例を挙げると、分散型偏微分方程式のStrichartzの評価式、Steinのrestriction予想、掛谷予想、Brascamp-Liebの不等式などです。最近、私はこの不等式の最適な定数に特に興味があります。例えば、熱流単調性 の方法などです。また、Bézier曲線と曲線と曲面のサブディビジョンを含む、計算幾何にも興味があります。

  • [1] Jonathan Bennett, Neal Bez, Susana Gutiérrez, Sanghyuk Lee, On the Strichartz estimates for the kinetic transport equation, to appear in Communications in Partial Differential Equations.
  • [2] Neal Bez, Mitsuru Sugimoto, Optimal constants and extremisers for some smoothing estimates, to appear in Journal d'Analyse Mathématique.
  • [3] Helmut E. Bez, Neal Bez, A note on magnitude bounds for the mask coefficients of the interpolatory Dubuc-Deslauriers subdivision scheme, to appear in LMS Journal of Computation and Mathematics.
  • [4] Neal Bez, Keith M. Rogers, A sharp Strichartz estimate for the wave equation with data in the energy space, Journal of the European Mathematical Society, 15 (2013), 805-823.

  • [5] Jonathan Bennett, Neal Bez, Some nonlinear Brascamp-Lieb inequalities and applications to harmonic analysis, Journal of Functional Analysis, 259 (2010), 2520-2556.

  • [6] Jonathan Bennett, Neal Bez, Closure properties of solutions to heat inequalities, Journal of Geometric Analysis, 19 (2009), 584-600.

  • [7] Jonathan Bennett, Neal Bez, Anthony Carbery, Dirk Hundertmark, Heat- flow monotonicity of Strichartz norms, Analysis & PDE, 2 (2009), 147-158.