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 「OPTIMAL HARDY-TYPE INEQUALITIES FOR SCHRÖDINGER FORMS」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。
リケラボ

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

OPTIMAL HARDY-TYPE INEQUALITIES FOR SCHRÖDINGER FORMS

Takeda, Masayoshi 大阪大学 DOI:10.18910/93059

2023.10

概要

for second-order non-negative elliptic operators on non-compact Riemannian manifolds, in
particular, they show that the criticality of Schr¨odinger forms is related to the critical Hardy
weights. In [20] we give a method to construct a critical Schr¨odinger form from a transient Dirichlet form by subtracting a suitable positive potential. In other words, we give a
method to construct critical Hardy weights for a transient Dirichlet form by applying the
idea in [6]. In this paper, we will consider subcritical Schr¨odinger forms instead of transient
Dirichlet forms, and extend the method for subcritical Schr¨odinger forms. As an application,
we obtain a method to construct critical Hardy weights for Schr¨odinger forms. Moreover,
we discuss the optimality of Hardy weights in the sense of [6], a stronger notion than the
criticality, and give a condition for the critical Hardy weights being optimal ones.
Let E be a locally compact separable metric space and m a positive Radon measure on
E with full topological support. Let X = (P x , Xt , ζ) be an m-symmetric Hunt process. We
assume that X is irreducible and resolvent doubly Feller, in addition, that X generates a
regular Dirichlet form (, ()) on L2 (E; m).
Denote by loc (X) the totality of local Kato measures (Definition 3.1 (1)). For a singed
local Kato measure such that the positive (resp. negative) part μ+ (resp. μ− ) of μ belongs to
2020 Mathematics Subject Classification. Primary 31C25; Secondary 26D15, 31C05. ...

論文の公開元へ

この論文で使われている画像

関連論文

関連論文をもっと見る

参考文献

[1] S. Albeverio and Z-M. Ma: Perturbation of Dirichlet forms-lower semiboundedness, closability, and form

cores, J. Funct. Anal. 99 (1991), 332–356.

[2] J. Cao, A. Grigor’yan and L. Liu: Hardy’s inequality and Green function on metric measure spaces, J.

Funct. Anal. 281 (2021), Paper No. 109020, 78 pp.

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

[4] Z.-Q. Chen and M. Fukushima: Symmetric Markov Processes, Time Change, and Boundary Theory, London Math. Soc. Monographs Series 35, Princeton University Press, Princeton, 2012.

[5] E.B. Davies: Heat Kernels and Spectral Theory, Cambridge Univ. Press, Cambridge, 1989.

[6] B. Devyver, M. Fraas and Y. Pinchover: Optimal Hardy weight for second-order elliptic operator: an

answer to a problem of Agmon, J. Funct. Anal. 266 (2014), 4422–4489.

[7] P.J. Fitzsimmons: Hardy’s inequality for Dirichlet forms, J. Math. Anal. Appl. 250 (2000), 548–560.

[8] R.L. Frank, D. Lenz and D. Wingert: Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory, J. Funct. Anal. 266 (2014), 4765–4808.

[9] M. Fukushima, Y. Oshima and M. Takeda: Dirichlet Forms and Symmetric Markov Processes, 2nd ed.,

Walter de Gruyter, Berlin, 2011.

[10] M. Keller, Y. Pinchover and F. Pogorzelski: Criticality theory for Schr¨odinger operators on graphs, J.

Spectr. Theory 10 (2020), 73–114.

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

[12] H. Kovarik and Y. Pinchover: On minimal decay at infinity of Hardy-weights, Commun. Contemp. Math.

22 (2020), Paper No. 1950046, 18 pp.

[13] M. Kurniawaty, K. Kuwae and K. Tsuchida: On the doubly Feller property of resolvent, Kyoto J. Math. 57

(2017), 637–654.

[14] Y. Miura: Optimal Hardy inequalities for Schr¨odinger operators based on symmetric stable processes, J.

Theoret. Probab. 36 (2023), 134–166.

[15] M. Schmidt: (Weak) Hardy and Poincar´e inequalities and criticality theory, Dirichlet forms and related

topics, Springer Proc. Math. Stat. 394 Springer, Singapore, 2022, 421–460.

[16] B. Schmuland: Extended Dirichlet spaces, C. R. Math. Acad. Sci. Soc. R. Can. 21 (1999), 146–152.

[17] B. Schmuland: Positivity preserving forms have the Fatou property, Potential Anal. 10 (1999), 373–378.

[18] M. Silverstein: Symmetric Markov processes, Lecture Notes in Mathematics 426, Springer-Verlag, BerlinNew York, 1974.

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

776

M. Takeda

[20] M. Takeda and T. Uemura: Criticality of Schr¨odinger forms and recurrence of Dirichlet forms, Trans.

Amer. Math. Soc. 376 (2023), 4145–4171.

Department of Mathematics

Kansai University

Yamatecho, Suita, 564–8680

Japan

e-mail: mtakeda@kansai-u.ac.jp

...

参考文献をもっと見る

全国の大学の
卒論・修論・学位論文
を
一発検索！

この論文の関連論文を見る