Wakabayashi, Seiichiro

professor emeritus

University of Tsukuba

Email:

Research Interests

Hyperbolic operators and Microlocal analysis

Recent Publications

• On the Cauchy problem for hyperbolic operators with triple characteristics whose coefficients depend only on the time variable, Tsukuba J. Math. 49-1 (2025), 1-50 pdf  new!
• On the Cauchy problem for hyperbolic operators with triple characteristics whose coefficients depend only on the time variable Tsukuba J. Math. 49-1 (2025), 51-105 pdf  new!
• 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 +…+ξ_n-1² +x_n²ξ_n² 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) (This is divided into two paperes and published in Tsukuba J. Math.)

Notes

• On well-posedness in Gevrey classes of the Cauchy problem for hyperbolic operators of second order (examples) pdf  (version on 2024/12/4)  new!
• 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

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