Hiroyuki Chihara

College of Education
University of the Ryukyus
Nishihara, Okinawa 903-0213, Japan

Hiroyuki Chihara is a Japanese mathematician who had been working on partial differential equations and geometric analysis, in particular the analysis of dispersive partial differential differential equations on the Euclidean space and dispersive flows from Riemannian manifolds to almost Hermitian manifolds. He thought it was interesting to see the invisible inside by measuring the outside, so he started research on microlocal analysis of integral geometry in 2020. Roughly speaking, this is an area of mathematics research related to the mathematical principles of CT scanners. He is also interested in medical imaging, security inspection, seismology, ocean science, non-line-of-sight imaging, data science, computational science and other applied mathematics related to his current research field. He usually prefers computers with Debian based operating system such as Ubuntu, and likes software such as MATLAB, Julia Programming Language, Mathematica and Maxima. He is currently a general member of AMS and SIAM.

• Recent Talks
• Papers and Preprints
1. Microlocal analysis of d-plane transform on the Euclidean space, SIAM J. Math. Anal., 54(6) (2022), pp.6254-6287, doi.
2. Bargmann transform on the space of hyperplanes, J. Fourier Anal. Appl., 28 (2022), article No.72, 21 pages, doi.
3. Inversion of higher dimensional Radon transforms of seismic-type, Vietnam Journal of Mathematics, 49 (2021), pp.1185-1198, doi.
4. Inversion of seismic-type Radon transforms on the plane, Integral Transforms Spec. Funct., 31 (2020), pp.998-1009, doi.
5. Bargmann-type transforms and modified harmonic oscillators, Bull. Malays. Math. Sci. Soc., 43 (2020), pp.1719-1740, doi.
6. Holomorphic Hermite functions in Segal-Bargmann spaces, Complex Anal. Oper. Theory, 13 (2019), pp.351-374, doi.
7. Joint work with Takashi Furuya and Takumi Koshikawa, Hermite expansions of some tempered distributions, J. Pseudo-Differ. Oper. Appl., 9 (2018), pp.105-124, doi.
8. Holomorphic Hermite functions and ellipses, Integral Transforms Spec. Funct. 28 (2017), pp.605-615, doi.
9. Fourth-order dispersive systems on the one-dimensional torus, J. Pseudo-Differ. Oper. Appl., 6 (2015), pp.237-263, doi.
10. Joint work with Eiji Onodera, A fourth-order dispersive flow into Kähler manifolds, Z. Anal. Anwend., 34 (2015), pp.221-249, doi.
11. Schrödinger flow into almost Hermitian manifolds, Bull. Lond. Math. Soc., 45 (2013), pp.37-51, doi.
12. Joint work with Eiji Onodera, A third order dispersive flow for closed curves into almost Hermitian manifolds, J. Funct. Anal., 257 (2009), pp.388-404, doi.
13. Bounded Berezin-Toeplitz operators on the Segal-Bargmann space, Integral Equations Operator Theory, 63 (2009), pp.321-335, doi.
14. Gain of analyticity for semilinear Schrödinger equations, J. Differential Equations, 246 (2009), pp.681-723, doi.
15. Resolvent estimates related with a class of dispersive equations, J. Fourier Anal. Appl., 14 (2008), pp.301-325, doi.
16. The initial value problem for a third order dispersive equation on the two dimensional torus, Proc. Amer. Math. Soc., 133 (2005), pp.2083-2090, doi.
17. The initial value problem for Schrödinger equations on the torus, Int. Math. Res. Not., 2002:15 (2002), pp.789-820, doi.
18. Smoothing effects of dispersive pseudodifferential equations, Comm. Partial Differential Equations, 27 (2002), pp.1953-2005, doi.
19. Gain of regularity for semilinear Schrödinger equations, Math. Ann., 315 (1999), pp.529-567, doi.
20. The initial value problem for the elliptic-hyperbolic Davey-Stewartson equation, J. Math. Kyoto Univ., 39 (1999), pp.41-66, doi.
21. The initial value problem for cubic semilinear Schrödinger equations, Publ. Res. Inst. Math. Sci., 32 (1996), pp.445-471, doi.
22. Global existence of small solutions to semilinear Schrödinger equations, Comm. Partial Differential Equations, 21 (1996), pp.63-78, doi.
23. Global existence of small solutions to semilinear Schrödinger equations with gauge invariance, Publ. Res. Inst. Math. Sci., 31 (1995), pp.731-753, doi.
24. Local existence for semilinear Schrödinger equations, Math. Japon., 42 (1995), pp.35-52, url.
25. Local existence for the semilinear Schrödinger equations in one space dimension, J. Math. Kyoto Univ., 34 (1994), pp.353-367, doi.

• Refereed Conference Papers
1. Smoothing effects of dispersive pseudodifferential equations, Report, Mathematisches Forschungsinstitut Oberwolfach, 20 (2002), pp.2-3.
2. The initial value problem for semilinear Schrödinger equations, GAKUTO Internat. Ser. Math. Sci. Appl., 10 (1997), pp.19-24.

• Names of TeX files of recent papers
• used:   laksa (2017), haze (2018), otah (2019), meepok (2019), gapao rice (2020), wanton mee (2021).
• unused:   poh, satay, nasi lemak, lapis sagu, kuih/kue talam, hokkien mee, mee goreng, nasi goreng, kao mun gai, char kway teow, hainanese chicken rice, ...

• English pronunciation of linux

• Update of Julia Programming Language for linux
• Set paths
sudo rm -rf /usr/local/bin/julia
sudo ln -s /usr/local/share/julia-1.8.3/bin/julia /usr/local/bin/julia
• Jupyter notebook