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)

[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 -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] null-solutions for some non-Fuchsian operators with
coefficients,

*Bull. Fac. Gen. Educ., Gifu Univ.*, Vol.**22**(1986), 95-100.
(resume(Japanese:JIS).)

[ 9] Existence of
null-solutions and behavior of
bicharacteristic curves for differential operators with
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
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 L_{p}(**R**^{n}),
*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.

[26]

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(C) Takeshi MANDAI 2002-2008.