Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya On the singularity structure of WKB solution of the boosted Whittaker equation: its relevance to resurgent functions with essential singularities. (English) Zbl 1372.34140 Lett. Math. Phys. 106, No. 12, 1791-1815 (2016). Reviewer: Yoshitsugu Takei (Kyoto) MSC: 34M60 34M30 34M40 PDFBibTeX XMLCite \textit{S. Kamimoto} et al., Lett. Math. Phys. 106, No. 12, 1791--1815 (2016; Zbl 1372.34140) Full Text: DOI
Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya Resurgent functions and linear differential operators of infinite order – Their happy marriage in exact WKB analysis. (English) Zbl 1329.34142 RIMS Kôkyûroku Bessatsu B52, 127-146 (2014). MSC: 34M60 34M30 34E20 PDFBibTeX XMLCite \textit{S. Kamimoto} et al., RIMS Kôkyûroku Bessatsu B52, 127--146 (2014; Zbl 1329.34142)
Kamimoto, Shingo; Kawai, Takahiro; Takei, Yoshitsugu Microlocal analysis of fixed singularities of WKB solutions of a Schrödinger equation with a merging triplet of two simple poles and a simple turning point. (English) Zbl 1279.34105 Sabadini, Irene (ed.) et al., The mathematical legacy of Leon Ehrenpreis. Berlin: Springer (ISBN 978-88-470-1946-1/hbk; 978-88-470-1947-8/ebook). Springer Proceedings in Mathematics 16, 125-150 (2012). MSC: 34M60 34L40 81Q20 PDFBibTeX XMLCite \textit{S. Kamimoto} et al., Springer Proc. Math. 16, 125--150 (2012; Zbl 1279.34105) Full Text: DOI
Kawai, Takahiro; Koike, Tatsuya; Takei, Yoshitsugu On the exact WKB analysis of higher order simple-pole type operators. (English) Zbl 1231.34155 Adv. Math. 228, No. 1, 63-96 (2011). Reviewer: Andrei A. Kapaev (Trieste) MSC: 34M60 47B40 PDFBibTeX XMLCite \textit{T. Kawai} et al., Adv. Math. 228, No. 1, 63--96 (2011; Zbl 1231.34155) Full Text: DOI
Kashiwara, Masaki; Kawai, Takahiro Professor Mikio Sato and microlocal analysis. (English) Zbl 1223.32005 Publ. Res. Inst. Math. Sci. 47, No. 1, 11-17 (2011). Reviewer: Gheorghe Gussi (Bucureşti) MSC: 32A45 32C38 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{T. Kawai}, Publ. Res. Inst. Math. Sci. 47, No. 1, 11--17 (2011; Zbl 1223.32005) Full Text: DOI
Aoki, Takashi; Kawai, Takahiro; Koike, Tatsuya; Takei, Yoshitsugu On the exact WKB analysis of microdifferential operators of WKB type. (English) Zbl 1079.34070 Ann. Inst. Fourier 54, No. 5, 1393-1421 (2004). Reviewer: J. Saurer (Regensburg) MSC: 34M60 34M25 34M35 35A27 PDFBibTeX XMLCite \textit{T. Aoki} et al., Ann. Inst. Fourier 54, No. 5, 1393--1421 (2004; Zbl 1079.34070) Full Text: DOI Numdam Numdam EuDML
Kawai, Takahiro; Takei, Yoshitsugu WKB analysis of Painlevé transcendents with a large parameter. III: Local reduction of 2-parameter Painlevé transcendents. (English) Zbl 0901.34057 Adv. Math. 134, No. 1, 178-218 (1998). Reviewer: V.Burjan (Praha) MSC: 34E20 34L40 PDFBibTeX XMLCite \textit{T. Kawai} and \textit{Y. Takei}, Adv. Math. 134, No. 1, 178--218 (1998; Zbl 0901.34057) Full Text: DOI
Kawai, Takahiro; Takei, Yoshitsugu Secular equations through the exact WKB analysis. (English) Zbl 0834.34068 Boutet de Monvel, Louis (ed.), Analyse algébrique des perturbations singulières. I. Méthodes résurgentes. Conférences du symposium franco-japonais sur l’analyse algébrique des perturbations singulières, CIRM, Marseille-Luminy, France, October 20-26, 1991. Paris: Hermann. Trav. Cours. 47, 85-102 (1994). Reviewer: V.Burjan (Praha) MSC: 34E20 34L40 PDFBibTeX XMLCite \textit{T. Kawai} and \textit{Y. Takei}, in: Analyse algébrique des perturbations singulières. I. Méthodes résurgentes. Conférences du symposium franco-japonais sur l'analyse algébrique des perturbations singulières, CIRM, Marseille-Luminy, France, October 20-26, 1991. Paris: Hermann. 85--102 (1994; Zbl 0834.34068)
Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu WKB analysis, period integrals, deformations, \(\ldots\). (Japanese) Zbl 0966.34502 Kawai, Takahiro (ed.) et al., Algebraic analysis and number theory. Proceedings of a symposium held at the Research Institute for Mathematical Sciences, Kyoto University, Kyoto, March 23-28, 1992. Kyoto: Kyoto Univ., Research Inst. for Mathematical Sciences, RIMS Kôkyûroku. No. 810, 102-127 (1992). MSC: 34E20 32G34 34L40 81Q20 PDFBibTeX XMLCite \textit{T. Aoki} et al., in: Algebraic analysis and number theory. Proceedings of a symposium held at the Research Institute for Mathematical Sciences, Kyoto University, Kyoto, March 23-28, 1992. Kyoto: Kyoto Univ., Research Inst. for Mathematical Sciences. 102--127 (1992; Zbl 0966.34502)
Kashiwara, Masaki; Kawai, Takahiro; Takei, Yoshitsugu The structure of cohomology groups associated with the theta-zerovalues. (English) Zbl 1138.32300 Berenstein, Carlos A. (ed.) et al., Geometrical and algebraical aspects in several complex variables. Papers from the conference, Cetraro, Italy, June 1989. Rende: Editoria Elettronica. Semin. Conf. 8, 169-189 (1991). Reviewer: José M. Muñoz Porras (Salamanca) MSC: 32C38 14K25 35A27 PDFBibTeX XMLCite \textit{M. Kashiwara} et al., Semin. Conf. 8, 169--189 (1991; Zbl 1138.32300)
Aoki, Takashi; Kashiwara, Masaki; Kawai, Takahiro On a class of linear differential operators of infinite order with finite index. (English) Zbl 0628.35003 Adv. Math. 62, 155-168 (1986). Reviewer: V.Deundjak MSC: 35A27 47F05 35A20 PDFBibTeX XMLCite \textit{T. Aoki} et al., Adv. Math. 62, 155--168 (1986; Zbl 0628.35003) Full Text: DOI
Kawai, Takahiro; Takei, Yoshitsugu On a closed range property of a linear differential operator. (English) Zbl 0607.35033 Proc. Japan Acad., Ser. A 62, 386-388 (1986). MSC: 35J55 47F05 58J15 32W05 35A30 35B45 PDFBibTeX XMLCite \textit{T. Kawai} and \textit{Y. Takei}, Proc. Japan Acad., Ser. A 62, 386--388 (1986; Zbl 0607.35033) Full Text: DOI
Kashiwara, Masaki; Kawai, Takahiro; Kimura, Tatsuo Foundations of algebraic analysis. Transl. from the Japanese by Goro Kato. (English) Zbl 0605.35001 Princeton Mathematical Series, 37. Princeton, New Jersey: Princeton University Press. XII, 254 p. $ 38.00 (1986). Reviewer: S.Prishchepionok MSC: 35-02 35S05 32A45 32C35 35G05 58J40 35L30 PDFBibTeX XML
Kawai, Takahiro The Fabry-Ehrenpreis gap theorem for hyperfunctions. (English) Zbl 0554.46017 Proc. Japan Acad., Ser. A 60, 276-278 (1984). MSC: 46F15 42B05 35A99 PDFBibTeX XMLCite \textit{T. Kawai}, Proc. Japan Acad., Ser. A 60, 276--278 (1984; Zbl 0554.46017) Full Text: DOI
Sato, Mikio; Kashiwara, Masaki; Kawai, Takahiro Linear Differential equations of infinite order and theta functions. (English) Zbl 0546.35047 Adv. Math. 47, 300-325 (1983). MSC: 35N99 35S99 33E99 46F15 PDFBibTeX XMLCite \textit{M. Sato} et al., Adv. Math. 47, 300--325 (1983; Zbl 0546.35047) Full Text: DOI
Kawai, Takahiro An example of a complex of linear differential operators of infinite order. (English) Zbl 0525.35082 Proc. Japan Acad., Ser. A 59, 113-115 (1983). MSC: 35R15 35N99 35C10 35S99 33E99 14F05 PDFBibTeX XMLCite \textit{T. Kawai}, Proc. Japan Acad., Ser. A 59, 113--115 (1983; Zbl 0525.35082) Full Text: DOI
Ehrenpreis, Leon; Kawai, Takahiro Poisson’s summation formula and Hamburger’s theorem. (English) Zbl 0499.10042 Publ. Res. Inst. Math. Sci. 18, 833-846 (1982). MSC: 11M35 11M06 11R42 PDFBibTeX XMLCite \textit{L. Ehrenpreis} and \textit{T. Kawai}, Publ. Res. Inst. Math. Sci. 18, 833--846 (1982; Zbl 0499.10042) Full Text: DOI
Kashiwara, Masaki; Kawai, Takahiro On holonomic systems of microdifferential equations. III: Systems with regular singularities. (English) Zbl 0505.58033 Publ. Res. Inst. Math. Sci. 17, 813-979 (1981). MSC: 58J10 32Sxx 35N10 32A45 47F05 58C10 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{T. Kawai}, Publ. Res. Inst. Math. Sci. 17, 813--979 (1981; Zbl 0505.58033) Full Text: DOI
[Noumi, Masatoshi; Uchikoshi, Keisuke; Ishii, Tadashi; Fujimoto, Yoshihisa; Morimoto, Mitsuo; Kawai, Takahiro; Kataoka, Kiyōmi; Aoki, Takashi; Komatsu, Hikosaburō; Mulase, Motohiko; Yano, Tamaki] Microfunctions and linear differential equations. VII. Proceedings of a Symposium held at the Research Institute for Mathematical Sciences, Kyoto University, Kyoto, March 24-26, 1980. (Japanese) Zbl 0562.46025 RIMS Kôkyûroku, 410. Kyoto: Kyoto University, Research Institute for Mathematical Sciences. II, 153 p. (1980). MSC: 46F15 46-06 35-06 58-06 58C07 PDFBibTeX XML
Kashiwara, Masaki; Kawai, Takahiro Second-microlocalization and asymptotic expansions. (English) Zbl 0458.46027 Complex analysis, microlocal calculus and relativistic quantum theory, Proc. Colloq., Les Houches 1979, Lect. Notes Phys. 126, 21-76 (1980). MSC: 46F99 41A60 81Q99 58J99 30E15 46F15 PDFBibTeX XML
Kashiwara, Masaki; Kawai, Takahiro On the characteristic variety of a holonomic system with regular singularities. (English) Zbl 0449.58019 Adv. Math. 34, 163-184 (1979). MSC: 58J15 14B05 14B07 32Q99 32Sxx 58J47 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{T. Kawai}, Adv. Math. 34, 163--184 (1979; Zbl 0449.58019) Full Text: DOI
Kawai, Takahiro Holomorphic perturbation of a system of micro-differential equations. (English) Zbl 0383.35050 Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 5, 581-586 (1978). MSC: 35N10 35S99 PDFBibTeX XMLCite \textit{T. Kawai}, Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 5, 581--586 (1978; Zbl 0383.35050) Full Text: Numdam EuDML
Kawai, Takahiro Invariance of cohomology groups under a deformation of an elliptic system of linear differential equations. (English) Zbl 0452.58024 Proc. Japan Acad., Ser. A 53, 144-145 (1977). MSC: 58H10 58J15 58J99 35J45 PDFBibTeX XMLCite \textit{T. Kawai}, Proc. Japan Acad., Ser. A 53, 144--145 (1977; Zbl 0452.58024) Full Text: DOI
Kashiwara, Masaki; Kawai, Takahiro; Stapp, Henry P. Micro-analytic structure of the S-matrix and related functions. (English) Zbl 0443.35059 Publ. Res. Inst. Math. Sci., Kyoto Univ. 12, Suppl., 141-146 (1977). MSC: 35P25 35Q99 47A40 PDFBibTeX XMLCite \textit{M. Kashiwara} et al., Publ. Res. Inst. Math. Sci. 12, 141--146 (1977; Zbl 0443.35059) Full Text: DOI
Kawai, Takahiro; Stapp, Henry P. Discontinuity formula and Sato’s conjecture. (English) Zbl 0368.35067 Publ. Res. Inst. Math. Sci., Kyoto Univ. 12, Suppl., 155-232 (1977). MSC: 35S99 70F20 PDFBibTeX XMLCite \textit{T. Kawai} and \textit{H. P. Stapp}, Publ. Res. Inst. Math. Sci. 12, 155--232 (1977; Zbl 0368.35067) Full Text: DOI
Kawai, Takahiro Extension of solutions of systems of linear differential equations. (English) Zbl 0366.58013 Publ. Res. Inst. Math. Sci., Kyoto Univ. 12, 215-227 (1976). MSC: 58J99 34A30 58J40 PDFBibTeX XMLCite \textit{T. Kawai}, Publ. Res. Inst. Math. Sci. 12, 215--227 (1976; Zbl 0366.58013) Full Text: DOI
Kashiwara, Masaki; Kawai, Takahiro Finiteness theorem for holonomic systems of micro-differential equations. (English) Zbl 0361.35064 Proc. Japan Acad. 52, 341-343 (1976). MSC: 35S99 35N99 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{T. Kawai}, Proc. Japan Acad. 52, 341--343 (1976; Zbl 0361.35064) Full Text: DOI
Kashiwara, M.; Kawai, T.; Oshima, T. Structure of a single pseudodifferential equation in a real domain. (English) Zbl 0318.35076 J. Math. Soc. Japan 28, 80-85 (1976). MSC: 35S05 PDFBibTeX XMLCite \textit{M. Kashiwara} et al., J. Math. Soc. Japan 28, 80--85 (1976; Zbl 0318.35076) Full Text: DOI
Kawai, Takahiro On the propagation of analyticity of solutions of systems of linear differential equations with constant coefficients. (English) Zbl 0357.46048 J. Fac. Sci., Univ. Tokyo, Sect. I A 22, 267-270 (1975). MSC: 46F15 47F05 35D99 PDFBibTeX XMLCite \textit{T. Kawai}, J. Fac. Sci., Univ. Tokyo, Sect. I A 22, 267--270 (1975; Zbl 0357.46048)
Kawai, Takahiro Pseudo-differential operators acting on the sheaf of microfunctions. (English) Zbl 0308.35082 Hyperfunct. theoret. Phys., Rencontre Nice 1973, Lect. Notes Math. 449, 54-69 (1975). MSC: 35S05 35N10 47Gxx 46F15 PDFBibTeX XML
Kashiwara, Masaki; Kawai, Takahiro Micro-hyperbolic pseudo-differential operators. (English) Zbl 0305.35086 Hyperfunct. theoret. Phys., Rencontre Nice 1973, Lect. Notes Math. 449, 70-82 (1975). MSC: 35S05 35L55 47Gxx PDFBibTeX XML
Kashiwara, Masaki; Kawai, Takahiro Micro-hyperbolic pseudo-differential operators. I. (English) Zbl 0305.35066 J. Math. Soc. Japan 27, 359-404 (1975). MSC: 35L30 35S10 35G10 35G99 65H10 46F15 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{T. Kawai}, J. Math. Soc. Japan 27, 359--404 (1975; Zbl 0305.35066) Full Text: DOI
Kashiwara, Masaki; Kawai, Takahiro Micro-local properties of \(\prod^n_{j=1}f^{S_j}_{j^+}\). (English) Zbl 0304.35068 Proc. Japan Acad. 51, 270-272 (1975). MSC: 35N99 46F15 14E15 58J99 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{T. Kawai}, Proc. Japan Acad. 51, 270--272 (1975; Zbl 0304.35068) Full Text: DOI
Kawai, Takahiro Removable singularities of solutions of systems of linear differential equations. (English) Zbl 0298.35043 Bull. Am. Math. Soc. 81, 461-463 (1975). MSC: 35N10 58J99 PDFBibTeX XMLCite \textit{T. Kawai}, Bull. Am. Math. Soc. 81, 461--463 (1975; Zbl 0298.35043) Full Text: DOI
Kashiwara, Masaki; Kawai, Takahiro; Oshima, Toshio Structure of cohomology groups whose coefficients are microfunction solution sheaves of systems of pseudo-differential equations with multiple characteristics. II. (English) Zbl 0307.35082 Proc. Japan Acad. 50, 549-550 (1974). MSC: 35S05 PDFBibTeX XMLCite \textit{M. Kashiwara} et al., Proc. Japan Acad. 50, 549--550 (1974; Zbl 0307.35082) Full Text: DOI
Kashiwara, Masaki; Kawai, Takahiro; Oshima, Toshio Structure of cohomology groups whose coefficients are microfunction solution sheaves of systems of pseudo-differential equations with multiple characteristics. I. (English) Zbl 0307.35081 Proc. Japan Acad. 50, 420-425 (1974). MSC: 35S05 PDFBibTeX XMLCite \textit{M. Kashiwara} et al., Proc. Japan Acad. 50, 420--425 (1974; Zbl 0307.35081) Full Text: DOI
Sato, Mikio; Kawai, Takahiro; Kashiwara, Masaki Microfunctions and pseudo-differential equations. (English) Zbl 0277.46039 Hyperfunctions pseudo-diff. Equations, Proc. Conf. Katata 1971, Lect. Notes Math. 287, 263-529 (1973). Reviewer: Gunter Bengel (Münster) MSC: 46F15 35S05 46-02 35-02 58J40 46M99 PDFBibTeX XML
Kawai, Takahiro Some applications of micro-local analysis to the global study of linear differential equations. (English) Zbl 0265.35062 Astérisque 2/3, 229-243 (1973). MSC: 35S05 35G05 35B99 58J40 PDFBibTeX XMLCite \textit{T. Kawai}, Astérisque 2, 229--243 (1973; Zbl 0265.35062)
Kawai, Takahiro On the global existence of real analytic solutions of linear differential equations. (English) Zbl 0258.35061 Hyperfunctions pseudo-diff. Equations, Proc. Conf. Katata 1971, Lect. Notes Math. 287, 99-121 (1973). MSC: 35S05 PDFBibTeX XML
Kawai, Takahiro Finite-dimensionality of cohomology groups attached to systems of linear differential equations. (English) Zbl 0256.35059 J. Math. Kyoto Univ. 13, 73-95 (1973). MSC: 35N10 35N05 58J10 58J99 PDFBibTeX XMLCite \textit{T. Kawai}, J. Math. Kyoto Univ. 13, 73--95 (1973; Zbl 0256.35059) Full Text: DOI
Sato, Mikio; Kawai, Takahiro; Kashiwara, Masaki On the structure of single linear pseudo-differential equations. (English) Zbl 0297.35069 Proc. Japan Acad. 48, 643-646 (1972). MSC: 35S05 33E99 PDFBibTeX XMLCite \textit{M. Sato} et al., Proc. Japan Acad. 48, 643--646 (1972; Zbl 0297.35069) Full Text: DOI
Kawai, Takahiro Theorems on the finite-dimensionality of cohomology groups. II. (English) Zbl 0256.35058 Proc. Japan Acad. 48, 287-289 (1972). MSC: 35N10 35N05 58J10 58J99 PDFBibTeX XMLCite \textit{T. Kawai}, Proc. Japan Acad. 48, 287--289 (1972; Zbl 0256.35058) Full Text: DOI
Kawai, Takahiro Theorems on the finite -dimensionality of cohomology groups. I. (English) Zbl 0249.58014 Proc. Japan Acad. 48, 70-72 (1972). MSC: 58J99 55N99 35R99 PDFBibTeX XMLCite \textit{T. Kawai}, Proc. Japan Acad. 48, 70--72 (1972; Zbl 0249.58014) Full Text: DOI
Kawai, Takahiro Construction of local elementary solutions for linear partial differential operators with real analytic coefficients. II: The case with complex principal symbols. (English) Zbl 0216.12401 Publ. Res. Inst. Math. Sci., Kyoto Univ. 7, 399-426 (1971). MSC: 35A27 35A20 47F05 65H10 PDFBibTeX XMLCite \textit{T. Kawai}, Publ. Res. Inst. Math. Sci. 7, 399--426 (1971; Zbl 0216.12401) Full Text: DOI
Kawai, Takahiro Construction of local elementary solutions for linear partial differential operators with real analytic coefficients. I: The case with real principal symbols. (English) Zbl 0216.12303 Publ. Res. Inst. Math. Sci., Kyoto Univ. 7, 363-397 (1971). MSC: 35A27 35A20 47F05 PDFBibTeX XMLCite \textit{T. Kawai}, Publ. Res. Inst. Math. Sci. 7, 363--397 (1971; Zbl 0216.12303) Full Text: DOI
Kawai, Takahiro Construction of a local elementary solution for linear partial differential operators. I, II. (English) Zbl 0216.12302 Proc. Japan Acad. 47, 19-23, 147-152 (1971). MSC: 35A27 35A20 65H10 47F05 PDFBibTeX XMLCite \textit{T. Kawai}, Proc. Japan Acad. 47, 19--23, 147--152 (1971; Zbl 0216.12302) Full Text: DOI
Kawai, Takahiro Construction of elementary solutions for I-hyperbolic operators and solutions with small singularities. (English) Zbl 0216.12301 Proc. Japan Acad. 46, 912-916 (1970). MSC: 35A27 35A20 65H10 47F05 PDFBibTeX XMLCite \textit{T. Kawai}, Proc. Japan Acad. 46, 912--916 (1970; Zbl 0216.12301) Full Text: DOI
Kawai, Takahiro On the theory of Fourier hyperfunctions and its applications to partial differential equations with constant coefficients. (English) Zbl 0212.46101 J. Fac. Sci. Univ. Tokyo, Sect. I A 17, 467-517 (1970). MSC: 46-02 42A38 46F05 47F05 42B05 PDFBibTeX XMLCite \textit{T. Kawai}, J. Fac. Sci., Univ. Tokyo, Sect. I A 17, 467--517 (1970; Zbl 0212.46101)