Traces of operators with integrable kernels
| dc.contributor | Graduate Program in Mathematics. | |
| dc.contributor.advisor | Gürel, Burak. | |
| dc.contributor.author | Başakoğlu, Engin. | |
| dc.date.accessioned | 2023-03-16T11:21:42Z | |
| dc.date.available | 2023-03-16T11:21:42Z | |
| dc.date.issued | 2016. | |
| dc.description.abstract | Trace class operators are compact operators whose singular values are absolutely summable. C. Brislawn proved in [1] and [2] that a trace formula for trace class operator on L2(X) is determined by it's corresponding kernel where X Rn {u100000} in [1] or X is countably generated measure space {u100000} in [2] . We will bene t from [1] and [2] in this thesis. Yet the main aim of this thesis is to establish tools in order to nd a trace formula for trace class operators on L2(X) with a kernel and to be given the proofs in detail by utilizing these tools. Once X Rn, proofs make use of Hardy-Littlewood Maximal Theorem; otherwise, when X is countably generated measure space, Hardy- Littlewood Maximal Theorem should be replaced by Doob's Maximal Theorem for martingales which is used to generalize the former results. | |
| dc.format.extent | 30 cm. | |
| dc.format.pages | vii, 51 leaves ; | |
| dc.identifier.other | MATH 2016 B37 | |
| dc.identifier.uri | https://digitalarchive.library.bogazici.edu.tr/handle/123456789/15287 | |
| dc.publisher | Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2016. | |
| dc.subject.lcsh | Integral equations -- Numerical solutions. | |
| dc.title | Traces of operators with integrable kernels |
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