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Song, Renming Feng, Liming Feng, Runhuan DeVille, Lee Lu, Qu 2016-11-10T18:42:55Z 2016-11-10T18:42:55Z 2018-11-11T10:15:19Z 2016-07-12 2016-08 In this thesis we consider two types of non-symmetric processes, which are similar to the symmetric α-stable process. We derive sharp estimates for the eigenfunctions of the Feynman- Kac semigroups of these two types of processes and established their intrinsic contractivities. Our methods are mainly probabilistic and depend essentially on the sharp estimates of heat kernels. Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2018-08-01 The student, Qu Lu, accepted the attached license on 2016-07-11 at 15:10. The student, Qu Lu, submitted this Dissertation for approval on 2016-07-11 at 15:26. This Dissertation was approved for publication on 2016-07-12 at 09:47. DSpace SAF Submission Ingestion Package generated from Vireo submission #9871 on 2016-11-10 at 12:25:09 Made available in DSpace on 2016-11-10T18:42:55Z (GMT). No. of bitstreams: 3 LU-DISSERTATION-2016.pdf: 503180 bytes, checksum: 29a85f6729302901139ecc21047f9cd7 (MD5) LICENSE.txt: 4202 bytes, checksum: c4346e7e50e257729d1e7dff743ff798 (MD5) PROQUEST_LICENSE.txt: 4548 bytes, checksum: 55102ccecbce72c32db5d839cdadccd1 (MD5) Previous issue date: 2016-07-12 Embargo set by: Seth Robbins for item 95475 Lift date: 2018-11-10T18:43:22Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system U of I Only Restriction Lifted for Item 95475 on 2018-11-11T10:15:19Z. application/pdf http://hdl.handle.net/2142/93052 en Copyright 2016 Qu Lu intrinsic contractivity non-symmetric semigroups non-local operators ground state domination Intrinsic contractivity for some non-symmetric Lévy processes with non-local operators text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.