{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T07:03:31Z","timestamp":1773903811957,"version":"3.50.1"},"reference-count":17,"publisher":"Mathematical Society of Japan (Project Euclid)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Soc. Japan"],"published-print":{"date-parts":[[2006,7,1]]},"DOI":"10.2969\/jmsj\/1156342040","type":"journal-article","created":{"date-parts":[[2007,11,20]],"date-time":"2007-11-20T16:33:02Z","timestamp":1195576382000},"source":"Crossref","is-referenced-by-count":13,"title":["The second term of the semi-classical asymptotic expansion for Feynman path integrals with integrand of polynomial growth"],"prefix":"10.2969","volume":"58","author":[{"given":"Daisuke","family":"FUJIWARA","sequence":"first","affiliation":[]},{"given":"Naoto","family":"KUMANO-GO","sequence":"additional","affiliation":[]}],"member":"1529","reference":[{"key":"1","doi-asserted-by":"publisher","unstructured":"G. D. Birkhoff, Quantum mechanics and asymptotic series, Bull. Amer. Math. Soc., <b>39<\/b> (1933), 681\u2013700.","DOI":"10.1090\/S0002-9904-1933-05716-6"},{"key":"2","doi-asserted-by":"crossref","unstructured":"R. H. Cameron, A family of integrals serving to connect the Wiener and Feynman integrals, J. Math. Phys., <b>39<\/b> (1960), 126\u2013140.","DOI":"10.1002\/sapm1960391126"},{"key":"3","doi-asserted-by":"crossref","unstructured":"C. P. Enz, Pauli lectures on Physics, (ed. C. P. Enz), <b>6<\/b>, MIT Press, 1973.","DOI":"10.1063\/1.3128362"},{"key":"4","doi-asserted-by":"publisher","unstructured":"R. P. Feynman, Space time approach to non relativistic quantum mechanics, Rev. Modern Phys., <b>20<\/b> (1948), 367\u2013387.","DOI":"10.1103\/RevModPhys.20.367"},{"key":"5","doi-asserted-by":"publisher","unstructured":"D. Fujiwara, A construction of fundamental solutions for Schr\u00f6dinger equations, Journal d'Analyse Math\u00e9matique, <b>35<\/b> (1979), 41\u201396.","DOI":"10.1007\/BF02791062"},{"key":"6","doi-asserted-by":"publisher","unstructured":"D. Fujiwara, Remarks on convergence of some Feynman path integrals, Duke Math. J., <b>47<\/b> (1980), 559\u2013600.","DOI":"10.1215\/S0012-7094-80-04734-1"},{"key":"7","doi-asserted-by":"publisher","unstructured":"D. Fujiwara, Some Feynman path integrals as oscillatory integrals over a Sobolev manifold, In: Functional analysis and related topics, (ed. H. Komatsu), Lecture Notes in Math., <b>1540<\/b>, Springer, 1991, pp.,39\u201353.","DOI":"10.1007\/BFb0085473"},{"key":"8","doi-asserted-by":"crossref","unstructured":"D. Fujiwara, The stationary phase method with an estimate of the remainder term on a space of large dimensions, Nagoya Math. J., <b>124<\/b> (1991), 61\u201397.","DOI":"10.1017\/S0027763000003780"},{"key":"9","unstructured":"D. Fujiwara, Mathematical theory of Feynman path integrals, Springer, Tokyo, 1999."},{"key":"10","doi-asserted-by":"publisher","unstructured":"D. Fujiwara and N. Kumano-go, Smooth functional derivatives in Feynman path integrals by time slicing approximation, Bull. Sci. Math., <b>129<\/b> (2005), 57\u201379.","DOI":"10.1016\/j.bulsci.2004.09.003"},{"key":"11","doi-asserted-by":"publisher","unstructured":"D. Fujiwara and N. Kumano-go, An improved remainder estimate of stationary phase method for some osicillatory integrals over a space of large dimension, Funkcial. Ekva., <b>49<\/b> (2006), 59\u201386.","DOI":"10.1619\/fesi.49.59"},{"key":"12","doi-asserted-by":"publisher","unstructured":"D. Fujiwara and T. Tsuchida, The time slicing approximation of the fundamental solution for the Schr\u00f6dinger equation with electromagnetic fields, J. Math. Soc. Japan, <b>40<\/b> (1997), 299\u2013327.","DOI":"10.2969\/jmsj\/04920299"},{"key":"13","unstructured":"G. W. Johnson and M. L. Lapidus, The Feynman integral and Feynman's operational calculus, Clarendon Press, Oxford, 2000."},{"key":"14","unstructured":"H. Kitada and H. Kumano-go, A family of Fourier integral operators and the fundamental solution for a Schr\u00f6dinger equation, Osaka J. Math., <b>18<\/b> (1981), 291\u2013360."},{"key":"15","doi-asserted-by":"publisher","unstructured":"N. Kumano-go, Feynman path integrals as analysis on path space by time slicing approximation, Bull. Sci. Math., <b>128<\/b> (2004), 197\u2013251.","DOI":"10.1016\/j.bulsci.2004.01.002"},{"key":"16","doi-asserted-by":"crossref","unstructured":"T. Tsuchida, Remarks on Fujiwara's stationary phase method on a space of large dimension with a phase function involving electromagnetic fields, Nagoya Math. J., <b>136<\/b> (1994), 157\u2013189.","DOI":"10.1017\/S0027763000025009"},{"key":"17","doi-asserted-by":"publisher","unstructured":"K. Yajima, Schr\u00f6dinger evolution equations with magnetic fields, Journal d'Analyse Math\u00e9matique, <b>56<\/b> (1991), 29\u201376.","DOI":"10.1007\/BF02820459"}],"container-title":["Journal of the Mathematical Society of Japan"],"original-title":[],"deposited":{"date-parts":[[2021,5,9]],"date-time":"2021-05-09T15:28:55Z","timestamp":1620574135000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/journal-of-the-mathematical-society-of-japan\/volume-58\/issue-3\/The-second-term-of-the-semi-classical-asymptotic-expansion-for\/10.2969\/jmsj\/1156342040.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,7,1]]},"references-count":17,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2006,7,1]]}},"URL":"https:\/\/doi.org\/10.2969\/jmsj\/1156342040","relation":{},"ISSN":["0025-5645"],"issn-type":[{"value":"0025-5645","type":"print"}],"subject":[],"published":{"date-parts":[[2006,7,1]]}}}