professor emeritus |

University of Tsukuba |

Email: |

Last modified: February 3, 2023

Hyperbolic operators and Microlocal analysis

- On the Cauchy Problem for hyperbolic operators with double characteristics whose principal parts have time dependent coefficients, Funkcialaj Ekvacioj 63 (2020), 345-418 pdf
- On the Cauchy problem for a class of hyperbolic operators whose coefficients depend only on the time variable, Tsukuba J. Math.@39-1 (2015), 121-163
- Singularities of solutions to the Cauchy problem for a class of second-order hyperbolic operators, Funkcialaj Ekvacioj 57 (2014), 375-448
- On the Cauchy problem for second-order hyperbolic operators with the coefficients of their principal parts depending only on the time variable, Funkcialaj Ekvacioj 55 (2012), 99-136
- On the Cauchy problem for hyperbolic operators of second order whose coefficients depend only on the time variable, J. Math. Soc. Japan 62-1 (2010), 95-133
- On the Cauchy problem for hyperbolic operators with nearly constant coefficient principal part, Funkcialaj Ekvacioj 51 (2008), 395-430
- Remarks on hyperbolic systems of first order with constant coefficient characterristic polynomials, Osaka J. Math. 44 (2007), 363-397
- Remarks on solvability of pseudo-differential operators in the space of hyperfunctions, J. Math. Sci. Univ. Tokyo 13 (2006), 595-616
- Remarks on first order hyperbolic systems with constant coefficient principal part, Annali dell'Università di Ferrara 52 (2006), 471-482
- Local solvability of operators with principal symbol ξ
_{1}^{2}+…+ξ_{n-1}^{2}+x_{n}^{2}ξ_{n}^{2}in the spaces of distributions and ultradistributions, Funkcialaj Ekvacioj 48-3 (2005), 453-487 - The C
^{∞}-well posed Cauchy problem for hyperbolic operators dominated by time functions, Japanese J. Math. 30-2 (2004), 283-348 (With K. Kajitani and K. Yagdjian) - The Cauchy problem for hyperbolic operators dominated by time functions, Hyperbolic Problems and Related Topics, 2003, pp423-436
- Remarks on analytic hypoellipticity and local solvability in the space of hyperfunctions, J. Math. Sci. Univ. Tokyo 10 (2003), 89-117
- On hypoellipticity of the operator exp[-|x
_{1}|^{-σ}] D_{1}^{2}+x_{1}^{4}D_{2}^{2}+1, Partial Differential Equations and Mathematical Physics in Memory of Jean Leray, Progress in Nonlinear Differential Equations and Their Applications, 2003, pp225-238 (With N. Nakazawa) - The hyperbolic operators with the characteristics vanishing with the different speeds, Osaka J. Math. 39-2 (2002), 447-485 (With K. Kajitani and K. Yagdjian)
- On hypoellipticity of the operator exp[-|x
_{1}|^{-σ}] D_{1}^{2}+x_{1}^{4}D_{2}^{2}+1, Publ. RIMS, Kyoto Univ. 38-1 (2002), 135-146 (With N. Nakazawa) - The Lax-Mizohata theorem for nonlinear Cauchy problems, Comm. in P. D. E. 26-7&8 (2001), 1367-1384
- Classical Microlocal Analysis in the Space of Hyperfunctions, Lecture Notes in
Mathematics, vol. 1737, Springer, 367pp, 2000

[errata for the above lecture note (pdf) (version on 2006/6/21)]

**Errata for my papers **pdf
(version on 2022/4/16)

- Remarks on propagation of analytic singularities and solvability in the space of microfunctions pdf (version on 2003/3/5)

- Puiseux expansions of the roots of the equations of pseudo-polynomials with a small parameter pdf (2019/1/16)
- Remarks on the conditions (L) and (L)
_{0}in the paper "On the Cauchy problem for hyperbolic operators with double characteristics whose principal parts have time dependent coefficients" pdf (2017/4/13) - Singularities of solutions to the Cauchy problem for second-order hyperbolic operators with the coefficients of their principal parts depending only on the time variable pdf (Preprint for Matsuyama Camp in 2011)
- Remarks on the composition formula for classical pseudo-differential operators pdf (the second version on 2012/3/16)
- Remarks on semi-algebraic functions II pdf (2010/9/6, misprints were corrected on 2018/8/2)
- Asymptotic expansions of the roots of the equations of pseudo-polynomials with a small parameter pdf (2008/4/24, misprints were corrected on 2013/5/14)
- Remarks on semi-algebraic functions pdf (2008/4/5) (version on 2010/8/30)
- T. Muramatu and S. Wakabayashi, On the norms of a symmetric multilinear form pdf (the second version on 2009/4/22)
- An alternative proof of Ivrii-Petkov's necessary condition for C
^{∞}well-posedness of the Cauchy problem pdf (2006/5/17) - Is there g(t)∈C
^{∞}(**R**) satisfying f(t)=g(t)^{2}when f(t)∈C^{∞}(**R**) and f(t)≥0? pdf (2006/5/19)

Domain of
Mathematics, University of Tsukuba