Takeshi MANDAI's Research Papers kao mark

(http://www.osakac.ac.jp/labs/mandai/mypapers.html ------ Last modified on June 04, 2008.)

Research Area :

1. Partial Differential Equations. Especially, (Characteristic) Cauchy Problems and Null-Solutions for Linear Partial Differential Equations.
2. Wavelet Analysis.

Lecture Notes in Japanese are listed in Miscellaneous Writings.

Some of these works were supported in part by Grant-in-Aid for Scientific Research (KAKENHI)
   Nos. 61540094(1986), 05640168(1993), 06640222(1994), 07640191(1995), 08640189(1996),
         10640157(1998,1999), 12640194(2000-2002), 15540188(2003,2004), 17540179(2005-2007), 20540193(2008-2010),
Japan Society for the Promotion of Science
(formerly, Japanese Ministry of Education, Culture, Sports, Science and Technology, or Japanese Ministry of Education, Science, Sports and Culture).

                          Click here to see resumes(Japanese:JIS)
The articles without author's names are written by Mandai, T.

[1] On energy inequalities and regularity of solutions to weakly hyperbolic Cauchy problems,
Publications of the Research Institute for Mathematical Sciences, Kyoto University(Publ. RIMS, Kyoto Univ.), Vol.18, No.2 (1982), 187-240. (resume(Japanese:JIS))

[ 2] Necessary conditions for well-posedness of the flat Cauchy problem and the regularity-loss of solutions,
Publ. RIMS, Kyoto Univ., Vol.19, No.1 (1983), 145-168. (resume(Japanese:JIS))
Typographical Errors

[ 3] A necessary and sufficient condition for the well-posedness of some weakly hyperbolic Cauchy problems,
Communications in Partial Differential Equations(Comm. in Partial Differ. Equations), Vol.8, No.7 (1983), 735-771. (resume(Japanese:JIS))

[ 4] On exceptional cases of Cauchy problems for Fuchsian partial differential operators,
Publ. RIMS, Kyoto Univ., Vol.20, No.5 (1984), 1007-1019. (resume(Japanese:JIS).)

[ 5] On the C infinity-well-posedness of Goursat problems,
Publ. RIMS, Kyoto Univ., Vol.21, No.4 (1985), 843-852. (resume(Japanese:JIS))

[ 6] Generalized Levi conditions for weakly hyperbolic equations --- an attempt to treat the degeneracy with respect to the space variables ---,
Publ. RIMS, Kyoto Univ., Vol.22, No.1 (1986), 1-23. (resume(Japanese:JIS).)

[ 7] Smoothness of roots of hyperbolic polynomials with respect to one-dimensional parameter,
Bulletin of the Faculty of General Education, Gifu University(Bull. Fac. Gen. Educ., Gifu Univ.), Vol.21(1985), 115-118. Scaned image of the reprint(pdf, 314KB) . (resume(Japanese:JIS).)

[ 8] C infinity null-solutions for some non-Fuchsian operators with C infinity coefficients,
Bull. Fac. Gen. Educ., Gifu Univ., Vol.22(1986), 95-100. (resume(Japanese:JIS).)

[ 9] Existence of C infinity null-solutions and behavior of bicharacteristic curves for differential operators with C infinity coefficients,
Japanese Journal of Mathematics(Japan. J. Math.), Vol.15, No.1 (1989), 53-63. (resume(Japanese:JIS).)

[10] Existence and non-existence of null-solutions for some non-Fuchsian partial differential operators with t-dependent coefficients,
Nagoya Mathematical Journal(Nagoya Math. J.), Vol.122(1991), 115-137. (resume(Japanese:JIS))

[11] Characteristic Cauchy problems for some non-Fuchsian partial differential operators,
Journal of the Mathematical Society of Japan (J. Math. Soc. Japan), Vol.45, No.3 (1993), 511--545. (resume(Japanese:JIS).)

[12] Existence of C infinity null-solutions for some differential operators with non-analytic coefficients,
Proceedings of the Fourth International Colloquium on Differential Equations, Plovdiv, Bulgaria, 18--23 August 1993, Vol.1, 147-162. (Edited by D.Bainov, V.Covachev, A.Dishliev. IMPLUS-M, Sofia, Bulgaria.) (Invited One-Hour Lecture at the Fourth International Colloquium on Differential Equations (1993.08.18--08.23), Plovdiv, Bulgaria.) (resume(Japanese:JIS).)
Preprint (English).

[13] Asymptotic solutions for exceptional cases of characteristic Cauchy problems to Fuchsian partial differential equations,
"Recent Developments in Evolution Equations", p.201--208, ed. by McBride/Roach, Pitman Research Notes in Mathematics Series 324, Longman Scientific & Technical, 1995. (Proceedings of the Conference on Evolution Equations, 07/25(Mon.)--29(Fri.), University of Strathclyde, Glasgow, Scotland, United Kingdom. )

[14] A Construction of Asymptotic Solutions and the Existence of Smooth Null-Solutions for a class of Non-Fuchsian Partial Differential Operators,
1997, Nagoya Math. J., 145(1997), 125--142. (resume(Japanese:JIS).)

[15] Asymptotic Solutions and Exact Solutions for Exceptional Cases of some Characteristic Cauchy Problems,
1998, Osaka J. Math., 35, 381--396. (resume(Japanese:JIS).)

[16] Existence of Distrubution Null-Solutions for Every Fuchsian Partial Differential OperatorsM,
J. Math. Sci. Univ. Tokyo, 5:1(1998), 1-18. (resume(Japanese:JIS).)

[17] Structure of Distribution Null-Solutions to Fuchsian Partial Differential Equations,
Equadiff 9: Conference on differential equations and their applications, Masaryk UNiversity, Brno, August 25--29, 1997. Equadiff 9 CD ROM: Abstracts and Enlarged Abstracts, p.141--142, 1998, edited by Z.Dosla, J.Kuben, J.Vosmansky. manuscript(pdf, 298KB).

[17'] Structure of Distribution Null-Solutions to Fuchsian Partial Differential Equations (Japanese),
1998, SuriKaiseki Kenkyusho Kokyuroku 1028, 52--66. Research Institute for Mathematical Sciences, Kyoto Univ. manuscript(pdf, 137KB)

[18] The Method of Frobenius to Fuchsian Partial Differential Equations,
2000, J. Math. Soc. Japan, 52:3, 645--672. Preprint Version (pdf, 253KB) (1999.02.22, Revised on 10.22)

[18'] Frobenius method for Fuchsian partial differential equations (Japanese),
1998, SuriKaiseki Kenkyusho Kokyuroku 1056, 29--39. Research Institute for Mathematical Sciences, Kyoto Univ. manuscript(pdf, 111KB)

[19] Mandai, T. - Tahara, H., Structure of solutions to Fuchsian systems of partial differential equations,
Nagoya Math. J., 169(2003), 1-17.

[19'] Mandai, T. - Tahara, H., Structure of the solutions to Fuchsian systems,
2002, SuriKaiseki Kenkyusho Kokyuroku 1261(2002), 68--77. Research Institute for Mathematical Sciences, Kyoto Univ.
Manuscript(pdf, 91KB, Fonts are different)

[20] Ashino, R. - Mandai, T., Wavelet Bases for Microlocal Filtering and the Sampling Theorem in Lp(Rn), Applicable Analysis, 82:1(2003), 1-24. (2003, Jan.)
Preprint Version: pdf, 666KB ; PostScript, 1,401KB ;

[21] Belarbi, M. - Mandai, T. - Mechab, M., Null-solutions for partial differential operators with several Fuchsian variables, Math. Nachr., 273, 3-13(2004).
Preprint Version: pdf, 358KB

[21'] Belarbi, M. - Mandai, T. - Mechab, M., Solutions nulles d'opérateurs aux dérivées partielles à plusieurs variables fuchsiennes, Comptes Rendus Mathematique (C. R. Acad. Sci. Paris - Series I - Mathematics), 336:4(2003), 315--318. pdf, 100KB

[22] Ashino, R. - Mandai, T. - Morimoto, A., System identification based on distribution theory and wavelet transform, Applicable Analysis, 84:2(2005), 165-195. (2005, Feb.)

[22'] Ashino, R. - Mandai, T. - Morimoto, A., Application of wavelet transform to system identification, Advances in pseudo-differential operators (Proceedings of Fourth ISAAC Congress 2003, Tronto), Series: Operator Theory: Advances and Applications, Vol.155, Birkh\"{a}user, Basel, 2004, 203-218.

[23] Belarbi, M. - Mandai, T. - Mechab, M., Global Fuchsian Goursat Problem in the Class of Holomorphic-Gevrey Functions, Osaka J. Math., 44:2(2007), 255-283.

[24] 芦野 隆一 - 萬代 武史 - 守本 晃, ウェーブレット解析のシステム同定への応用, 応用数理, 2007年3月25日 第17巻第1号, 2-13.

[25] Ashino, R. - Mandai, T. - Morimoto, A. - Sasaki, F., Blind Source Separation using time-frequency analysis, Fields Institute Communications 52(2007) "Pseudo-Differential Operators: Partial Differential Equations and time-Frequency Analysis", Ed. by L. Rodino - B.-W. Schulze - M.W. Wong, 401-414.

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(C) Takeshi MANDAI 2002-2008.