Daisuke Fujiwara

(藤原大輔)

Profile Information

Affiliation: Professor (Professor emeritus), Faculty of Science, Department of Mathematics, Gakushuin University Department of Mathematics, Gakushuin University

Degree: Doctor of science(The University of Tokyo)

J-GLOBAL ID: 200901005063521485
researchmap Member ID: 1000015869

External link: http://www.math.gakushuin.ac.jp/~fujiwara/

Research Interests

Research Areas

Education

Committee Memberships

1985 - 1990

ジャーナル編集委員、ジャーナル編集委員長、評議員、理事、理事長、監事, 日本数学会

Major Papers

Schrödinger方程式の基本解の構成:Feynman経路積分の収束

藤原大輔, 浅田健嗣

数学, 33(2) 97-119, 1981

その物理学における意義をさておくと,Feynman経路積分とは,数学的にはSchrodinger方程式の基本解の構成法であるとも考えられる.この小論では,そのような立場にたって,Feynman経路積分の定式化に際し,どのような困難があるかを説明し,いくつかの定式化の方法を紹介したい.

Misc.

Integration by parts formula for Feynman path integrals (Introductory Workshop on Path Integrals and Pseudo-Differential Operators)

Fujiwara Daisuke

RIMS Kokyuroku, 1958 1-24, Jul, 2015
Phase space Feynman path integrals via piecewise bicharacteristic paths and their semiclassical approximations (Exact WKB Analysis and Microlocal Analysis)

KUMANO-GO NAOTO, FUJIWARA DAISUKE

RIMS Kokyuroku Bessatsu, 37 113-136, Mar, 2013
Stationary Phase Method, Feynman Path Integrals and Integration by Parts Formula (Introductory Workshop on Feynman Path Integral and Microlocal Analysis)

FUJIWARA Daisuke

RIMS Kokyuroku, 1797 86-114, Jun, 2012
Smooth functional derivatives in Feynman path integrals by time slicing approximation (Hyperfunctions and linear differential equations 2006. History of Mathematics and Algorithms)

Kumano-go Naoto, Fujiwara Daisuke

RIMS Kokyuroku, 1648 32-52, May, 2009
Feynman Path Integrals and Semiclassical Approximation (Algebraic Analysis and the Exact WKB Analysis for Systems of Differential Equations)

KUMANO-GO Naoto, FUJIWARA Daisuke

RIMS Kokyuroku Bessatsu, 5 241-263, Jan, 2008
The second term of the semi-classical asymptotic expansion for Feynman path integrals with integrand of polynomial growth

Daisuke Fujiwara, Naoto Kumano-Go

Journal of the Mathematical Society of Japan, 58(3) 837-867, Jul, 2006
The second term of the semi-classical asymptotic expansion for Feynman path integrals with integrand of polynomial growth

Daisuke Fujiwara, Naoto Kumano-Go

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 58(3) 837-867, Jul, 2006
An improved remainder estimate of stationary phase method for some oscillatory integrals over a space of large dimension

Daisuke Fujiwara, Naoto Kumano-Go

FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 49(1) 59-86, Apr, 2006
An improved remainder estimate of stationary phase method for some oscillatory integrals over a space of large dimensions.

Daisuke Fujiwara, Naoto Kumano-go

Funkcialaj Ekvacioj., 49(1) 59-86, 2006
Smooth functional derivatives in Feynman path integrals by time slicing approximation

D Fujiwara, N Kumano-go

BULLETIN DES SCIENCES MATHEMATIQUES, 129(1) 57-79, Jan, 2005
Smooth funitional derivatives in Feynnian path integrals by time sliring approximutin, joint work with Natoto Kumanogo

Bulletin des Sciences Mathématique, in Press, 2004
熊ノ郷-谷口の定理の簡単な証明について (偏微分方程式の解の構造の研究)

藤原大輔, 熊ノ郷直人, 谷口和夫

数理解析研究所講究録, 1056 59-67, Aug, 1998
The time slicing approximation of the fundamental solution for the Schrodinger equation with electromagnetic fields

D Fujiwara, T Tsuchida

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 49(2) 299-327, Apr, 1997
A proof of estimates of Kumano-go-Taniguchi Type for Multiproduct of Fourier Integral Operators(共著)

Funkcialay Ekvacioj, 40(3) 459-470, 1997
The stationary phase method with remainder estimate as the dimension of the space goes to infinity

Proceedings of the Taniguchi symposium on Structure of solutions of differential equations,World Scientific, 129-134, 1996
The stationary phase method with remainder estimate as dimension of the space goes to infinity

D Fujiwara

PARTIAL DIFFERENTIAL OPERATORS AND MATHEMATICAL PHYSICS, 78 135-140, 1995
STATIONARY-PHASE METHOD WITH AN ESTIMATE OF THE REMAINDER TERM OVER A SPACE OF LARGE DIMENSION

D FUJIWARA

SPECTRAL AND SCATTERING THEORY, 161 1-14, 1994
Stationary phase method with estimate of remainder term over a space of large dimension

Advanced Studies in Pure Mathematics (日本数学会)、 Spectral and scattereing theory and applications, 23 57-67, 1994
Some Feynman path integrals as oscillatory integrals oun a Sobolev manifolds

FUJIWARA D.

Lecture notes in Springer Mathematies, 1540 39-53, 1993
THE STATIONARY PHASE METHOD WITH AN ESTIMATE OF THE REMAINDER TERM ON A SPACE OF LARGE DIMENSION

D FUJIWARA

NAGOYA MATHEMATICAL JOURNAL, 124 61-97, Dec, 1991
The stationary phase method with an estimate of the remainder term on a space of large dimension

Daisuke Fujiwara

Nagoya Mathematical Journal, 124 61-97, 1991
The Feynman path integral as an improper integral over the Sobolev space.

Proc. "Journee equation aux derivee partielles, Saint Jean de Monts", Soc. Math. France, 14, 1990
A CONSTRUCTION OF APPROXIMATE POSITIVE PARTS OF ESSENTIALLY SELFADJOINT PSEUDODIFFERENTIAL-OPERATORS

D FUJIWARA

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 37(1) 101-147, 1984
Remarks on convergenceof some Feynman path integrals

Duke Mathematical Journal, vol 47. pp 559-600., 1980
REMARKS ON CONVERGENCE OF THE FEYNMAN PATH-INTEGRALS

D FUJIWARA

DUKE MATHEMATICAL JOURNAL, 47(3) 559-600, 1980
A construction of fundamental solution for Schrodinger equations.

Journal d'analyse Mathematique, vol35,pp.41-96., 1979
On some oscillatory integral transformations in L²(Rⁿ).

Japanese J. Math., 4, 1979
A construction of the fundamental Solution for the Schrödinger equations

J. d'Analyses MathÉmatiques, 35, 1979
An Lr theorem of the Helmholz decomposition of vector fields. (with H. Morimoto)

J. Fac. Sci. Univ. Tokyo, vol. 24, 685-700, 1977
An L^r-theorem of the Helmholz decomposition of Vector fields,

J. Fac. Sc. Univ. Tokyo, 24, 1977
A relative Hodge-Kodaira decomposition

J. Math Soc. Japan, 24, 1972
On the asymptotic behaviour of the Green operators for elliptic boundary problems and the pure imaginary powers of some second order operators,

J. Math. Soc. Japan, 21, 1969
CONCRETE CHARACTARIZATION FOR DOMAIN OF FRACTIONAL POWERS OF SOME ELLIPTIC DIFFERENTIAL OPERATORS OF SECOND ORDER

PROCEEDING, JAPAN ACADEMY, 43, 426-428, 1967
CONCRETE CHARACTARIZATION FOR DOMAIN OF FRACTIONAL POWERS OF SOME ELLIPTIC DIFFERENTIAL OPERATORS OF SECOND ORDER

PROCEEDING, JAPAN ACADEMY, 43, 426-428, 1967
Concrete Charactiuzation for the Domani of Actuyal Powers of Some Elliptic Differential Apcrators of the Se***

Pros. Japan Acad, 43, 426-428, 1967
The asymptotic formula for the trace of elliptic operators on compact manifolds.

J. of the Fac Sci. Univ. of Tokyo, 15, 1967

Books and Other Publications

Rigorous time slicing approach to Feynman path integrals

藤原, 大輔

Springer, 2017 (ISBN: 9784431565512)
ファインマン経路積分の数学的方法

シュプリンガーフェアラーク東京, 1999

Professional Memberships

Research Projects

汎関数解析学とファインマン経路積分の数学的研究

科学研究費助成事業, 日本学術振興会, 2009 - 2009

藤原大輔
Mathematical Analysis of Quantum Physics

Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, 2006 - 2009

YAJIMA Kenji, FUJIWARA Daisuke, NAKAMURA Shu, MIZUTANI Akira, WATANABE Kazuo, SHIMOMURA Akihiro
Study of developing firm ability in Mathematics.

Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, 2004 - 2006

IITAKA Shigeru, FUJIWARA Daisuke, NAKAJIMA Shoichi, MIZUTANI Akira, KAWASAKI Tetsuro, OKABE Tsuneharu
Further Development of Trotter Product Formulas with Problems on Path Integrals

Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, 2004 - 2006

ICHINOSE Takashi, TAMURA Hiroshi, TAKANOBU Satoshi, FUJIWARA Daisuke, TAMURA Hideo, YAJIMA Kenji
Mathematical Analysis of Quantum Physics

Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, 2002 - 2005

YAJIMA Kenji, NAKAMURA Shu, FUJIWARA Daisuke, MIZUTANI Akira, WATANABE Kazuo, SHIIMOMURA Akihiro

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