| Budget Amount *help |
¥10,660,000 (Direct Cost: ¥8,200,000、Indirect Cost: ¥2,460,000)
Fiscal Year 2022: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2021: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2020: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2019: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2018: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Outline of Final Research Achievements |
We call symmetric Markov processes with tightness property Class (T) and propose that they are the next target to be considered, We show some sample path properties and spectral properties of generators.As an application, we show the existence and uniqueness of quasi-stationary distributions for symmetric Markov processes in Class (T). We construct a criticality theory of Schroedinger forms, The criticality and subcriticality of Schroedinger forms are regarded as generalized notions of the recurrence and transience of Dirichlet forms and critical Schroedinger forms are constructed by h-transform of recurrent Dirichlet forms. Critical Schroedinger forms lead to critical Hardy-type inequalities. Thus we obtain critical Hardy-type inequalities by h-transform of recurrent Dirichlet forms. As an application, we derive in unified manner optimal Hardy-type inequalities from Feller's recurrence criterion.
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