Wakabayashi, Seiichiro
professor emeritus |
University of Tsukuba |
Email: |
Last modified: February 27, 2024
Research Interests
Hyperbolic operators and Microlocal analysis
Recent Publications
- 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 ξ12
+…+ξn-12
+xn2ξn2
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[-|x1|-σ]
D12+x14
D22+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[-|x1|-σ]
D12+x14
D22+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 2023/11/19)
Preprints
- Remarks on propagation of analytic singularities and solvability in the space of microfunctions
pdf
(version on 2003/3/5)
- On the Cauchy problem for hyperbolic operators with triple characteristics whose coefficients depend only on the time variable
pdf
(version on 2024/2/27)
Notes
- 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
Pictures