リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

大学・研究所にある論文を検索できる 「GENERALIZED SCHRÖDINGER FORMS WITH APPLICATIONS TO MAXIMUM PRINCIPLES」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

コピーが完了しました

URLをコピーしました

論文の公開元へ論文の公開元へ
書き出し

GENERALIZED SCHRÖDINGER FORMS WITH APPLICATIONS TO MAXIMUM PRINCIPLES

Kim, Daehong 大阪大学 DOI:10.18910/83210

2021.07

概要

We study criticalities of generalized Schrödinger operators in terms of the Schrödinger forms induced by generalized Feynman-Kac perturbations of symmetric Markov processes, which extend earlier work due to Takeda [26]. The related functional inequalities and analytic characterizations of criticalities of Schrödinger forms are given. As applications, we establish some maximum principles via the analytic characterization.

参考文献

[1] H. Berestycki, L. Nirenberg and S.R.S. Varadhan: The principal eigenvalue and maximum principle for second-order elliptic operators in general domains, Comm. Pure Appl. Math. 47 (1994), 47–92.

[2] Z.-Q. Chen: Gaugeability and conditional gaugeability, Trans. Amer. Math. Soc. 354 (2002), 4639–4679.

[3] Z.-Q. Chen: Analytic characterization of conditional gaugeability for non-local Feynman-Kac transforms, J. Funct. Anal. 202 (2003), 226–246.

[4] Z.-Q. Chen, P.J. Fitzsimmons, K. Kuwae and T.-S. Zhang: Stochastic calculus for symmetric Markov processes, Ann. Probab. 36 (2008), 931–970.

[5] Z.-Q. Chen and K. Kuwae: On doubly Feller property, Osaka J. Math. 46 (2009), 909–930.

[6] Z.-Q. Chen and T.-S. Zhang: Girsanov and Feynman-Kac type transformations for symmetric Markov processes, Ann. Inst. H. Poincare Probab. Statist. ´ 38 (2002), 475–505.

[7] K.L. Chung and Z. Zhao: From Brownian motion to Schrodinger’s equation, Grundlehren der Mathema- ¨ tischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 312, Springer-Verlag, Berlin, 1995.

[8] G. De Leva, D. Kim and K. Kuwae: Lp-independence of spectral bounds of Feynman-Kac semigroups by continuous additive functionals, J. Funct. Anal. 259 (2010), 690–730.

[9] R.M. Dudley: Real Analysis and Probability, Cambridge Stud. Adv. Math. 74, Cambridge Univ. Press, Cambridge, 2002.

[10] M. Fukushima, Y. Oshima and M. Takeda: Dirichlet forms and symmetric Markov processes, Second revised and extended edition, de Gruyter Studies in Mathematics 19, Walter de Gruyter & Co., Berlin, 2011.

[11] R.K. Getoor: Transience and recurrence of Markov processes; in Seminar on Probability, XIV (Paris, 1978/1979) (French), 397–409, Lecture Notes in Math. 784, Springer, Berlin, Heidelberg, New York, 1980, 397–409.

[12] D. Kim, P. Kim and K. Kuwae: Stability of estimates for fundamental solutions under Feynman-Kac perturbations for symmetric Markov processes, (2020), preprint.

[13] D. Kim, M. Kurniawaty and K. Kuwae: A refinement of analytic characterizations of gaugeability for generalized Feynman-Kac functionals, Illinois J. Math. 59 (2015), 717–771.

[14] D. Kim and K. Kuwae: Analytic characterizations of gaugeability for generalized Feynman-Kac functionals, Trans. Amer. Math. Soc. 369 (2017), 4545–4596.

[15] D. Kim and K. Kuwae: General analytic characterization of gaugeability for Feynman-Kac functionals, Math. Ann. 370 (2018), 1–37.

[16] D. Kim, K. Kuwae and Y. Tawara: Large Deviation principle for generalized Feynman-Kac functionals and its applications, Tohoku Math. J. 68 (2016), 161–197.

[17] D. Kim and Y. Oshima: Some inequalities related to transience and recurrence of Markov processes and their applications, J. Theoret. Probab. 23 (2010), 148–168.

[18] M. Kurniawaty, K. Kuwae and K. Tsuchida: On the doubly Feller property of resolvent, Kyoto J. Math. 57 (2017), 637–654.

[19] N.S. Landkof: Foundations of Modern Potential Theory, Springer, New York-Heidelberg, 1972.

[20] L. Li: Criticality and subcriticality of generalized Schr¨odinger forms with non-local perturbations, Proc. Amer. Math. Soc. 145 (2017), 3929–3939.

[21] M. Murata: Structure of positive solutions to (−Δ + V)u = 0 in Rn, Duke Math. J. 53 (1986), 869–943.

[22] Y. Pinchover: Criticality and ground states for second-order elliptic equations, J. Differential Equations 80 (1989), 237–250.

[23] Y. Pinchover and K. Tintarev: A ground state alternative for singular Schr¨odinger operators, J. Funct. Anal. 230 (2006), 65–77.

[24] P. Stollmann and J. Voigt: Perturbation of Dirichlet forms by measures, Potential Anal. 5 (1996), 109–138.

[25] M. Takeda: A variational formula for Dirichlet forms and existence of ground states, J. Funct. Anal. 266 (2014), 660–675.

[26] M. Takeda: Criticality and subcriticality of generalized Schr¨odinger forms, Illinois J. Math. 58 (2014), 251–277.

[27] M. Takeda: Criticality for Schr ¨odinger type operators based on recurrent symmetric stable processes, Trans. Amer. Math. Soc. 368 (2016), 149–167.

[28] M. Takeda: The bottom of the spectrum of time-changed processes and the maximum principle of Schr¨odinger operators, J. Theoret. Probab. 31 (2018), 741–756.

[29] M. Takeda: Maximum principles for generalized Schr¨odinger equations, Illinois J. Math. 64 (2020), 119– 139.

[30] M. Takeda: Potential theory for Green functions of Schr¨odinger-type operators, Studia Math. 250 (2020), 109–127.

[31] M. Takeda and K. Tsuchida: Differentiability of spectral functions for symmetric α-stable processes, Trans. Amer. Math. Soc. 359 (2007), 4031–4054.

参考文献をもっと見る