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Proof of Theorem 1.3 - Part (i)

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Boundary Value Problems and Markov Processes

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1499))

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Abstract

This Chapter 8 and the next Chapter 9 are devoted to the proof of Theorem 1.3 and Theorem 1.4. In this chapter we prove part (i) of Theorem 1.3. In the proof we make use of Sobolev’s imbedding theorems (Theorems 8.1 and 8.2) and a λ-dependent localization argument due to Masuda [Ma] (cf. Lemma 8.4) in order to adjust estimate

$$\parallel (A_p - \lambda {\rm I})^{ - 1} \parallel \, \le \frac{{c_p (\varepsilon )}}{|\lambda| }\,\,for\,all\,\lambda \in \,\Sigma p(\varepsilon ) $$
(4)

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Correspondence to Kazuaki Taira .

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© 2009 Springer-Verlag Berlin Heidelberg

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Taira, K. (2009). Proof of Theorem 1.3 - Part (i). In: Boundary Value Problems and Markov Processes. Lecture Notes in Mathematics(), vol 1499. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01677-6_8

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