西谷達雄, Nishitani Tatsuo

Professor Emeritus

Department of Mathematics

Osaka University

Toyonaka, Osaka 560-0043

JAPAN

E-mail: nishitani@math.sci.osaka-u.ac.jp

List of publications

Recent Papers

- Notes on geometric aspects of effectively hyperbolic critical points when the characteristic roots are real on one side of time, Proc. Japan Acad. Ser. A Math.Sci. (2024) OpenAccess
- A more direct way to the Cauchy problem for effectively hyperbolic operators, J. Pseudo-Differ. Oper. Appl. (2024) shared link
- Cauchy problem for operators with triple effectively hyperbolic characteristics--Ivrii's conjecture--, J. Anal. Math. (2023) shared link
- A discrete algorithm for general weakly hyperbolic systems (with Ferruccio Colombini and Jeffrey Rauch) J. Pseudo-Differ. Oper. Appl. (2022) shared link
- Diagonal symmetrizers for hyperbolic operators with triple characteristics Mathematishe Annalen (2021) shared link
- Transversally strictly hyperbolic systems, Kyoto J. Math. 60 (2020), 1399-1418 pdf
- On the Cauchy problem for D_t^2-D_x(b(t)a(x))D_x, Journal of Hyperbolic Differential Equations (2020), 75-122 (with Ferruccio Colombini)
- Cauchy problem for hyperbolic operators with triple effective characteristics on the initial plane, Osaka J. Math. 57 (2020), 597-615 (with Vesselin Petkov)
- Notes on symmetrization by Bezoutian, Bollettino dell'Unione Matematica Italiana (2020) 13: 417-428 link
- Cauchy problem for effectively hyperbolic operators with triple characteristics, J. Math. Pures Appl., 123 (2019), 201-228 (with Vesselin Petkov)
- Weakly hyperbolic systems by symmetrization, Ann. Sci. Norm. Super. Pisa XIX (2019), 217-251 (with Ferruccio Colombini and Jeffrey Rauch)
- Note on strongly hyperbolic systems with involute characteristics, Kyoto J. Math., 58 (2018), 569-582 (with Guy M\'etivier) pdf

Preprints

- arXiv
- A direct energy estimates for effectively hyperbolic operators pdf
- Cauchy problem for operators with triple effectively hyperbolic characteristics--Ivrii's conjecture-- arxiv

講義録など

- The Cauchy problem for differential operators with double characteristics, Sugaku Expositions, AMS. 31(2018)pdf
- 二次特性的双曲型偏微分方程式の初期値問題の適切性(数学，2014) download
- Effectively hyperbolic Cauchy problem (Lectures at De Giorgi Center, 2004) pdf
- Hyperbolic equations with double characteristics (Lectures at University of Pisa, 2000) pdf
- Hyperbolic Systems with Two Independent Variables (Lectures at Tsukuba University, 1999) pdf
- 強双曲系ーその必要条件を探る(Lectures at Ryukoku University, 1997) pdf
- The hyperbolic Cauchy problem (Lectures at Seoul National University, 1992) pdf
- 基礎教養 pdf
- Calculus pdf
- Lebesgue 積分 pdf
- 擬微分作用素 pdf

Notes

- Examples of uniformly symmetrizable systems for which the Cauchy problem is ill-posed in the Gevrey class >2 (February, 2024) slides
- Applications of pseudodifferential operators of symbol exp(S^{\kappa}_{\rho,\delta}) to the Cauchy problem (February, 2024)pdf
- On pseudodifferential operators of symbol exp(S^{\kappa}_{\rho,\delta}) (January, 2024)pdf
- exp(S^{\kappa}_{\rho,\delta})型Gevrey擬微分作用素について (October, 2023)pdf
- A note on time functions associated with effectively hyperbolic double characteristics (March, 2022) pdf
- Notes on tangent bicharacteristics and transition of the spectral type of the Hamilton map (April, 2022) pdf
- A note on the Cauchy problem for -D
_{0}^{2}+2x_{1}D_{0}D_{2}+D_{1}^{2}+x_{1}^{3}D_{2}^{2}+b_{0}D_{0}+b_{1}D_{1}+b_{2}D_{2}(March, 2022) pdf - A question on the Cauchy problem in the Gevrey classes for weakly hyperbolic equations (July, 2022) pdf

Books

- 実効的双曲型作用素の初期値問題 (数学メモアール, 2024)
- Cauchy Problem for Differential Operators with Double Characteristics (LNM, Springer, 2017)
- Corrections
- 線形双曲型偏微分方程式 (朝倉書店, 2015)
- 正誤表
- Hyperbolic Systems With Analytic Coefficients (LNM, Springer, 2014)
- Corrections
- Cauchy Problem for Noneffectively Hyperbolic Operators (MSJ Memoirs, 2013)
- Corrections
- The effectively hyperbolic Cauchy problem (LNM, Springer, 1991)

Last modified: June 18, 2024