A boundary decay condition, called vanishing to infinite logarithmic order is introduced. A pseudodifferential calculus, extending the b-calculus of Melrose, is proposed based on this modest decay condition. The mapping properties, composition rule, and normal operators are studied. Instead of functional analytic methods, a geometric approach is invoked in pursuing the Fredholm criterion. As an application, a detailed proof of the Atiyah-Patodi-Singer index theorem, including a review of Dirac operators of product type and construction of the heat kernel, is presented.
","abstract_html":"<p>A boundary decay condition, called vanishing to infinite logarithmic order is introduced. A pseudodifferential calculus, extending the <em> b</em>-calculus of Melrose, is proposed based on this modest decay condition. The mapping properties, composition rule, and normal operators are studied. Instead of functional analytic methods, a geometric approach is invoked in pursuing the Fredholm criterion. As an application, a detailed proof of the Atiyah-Patodi-Singer index theorem, including a review of Dirac operators of product type and construction of the heat kernel, is presented.</p>","abstract_has_math":false,"creators":["Huang, Binbin"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":["Paul A. Loya"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-01-01T08:00:00Z","date_published":"2018-01-01T08:00:00Z","updated_at":"2026-07-24T01:10:09Z","subjects":["Pure sciences","B-calculus","Dirac operator","Heat kernel","Index theory","Pseudodifferential operator","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://orb.binghamton.edu/dissertation_and_theses/36","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Paul A. Loya"]},{"key":"dc:creator","label":"Author","values":["Huang, Binbin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Pure sciences","B-calculus","Dirac operator","Heat kernel","Index theory","Pseudodifferential operator","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://orb.binghamton.edu/dissertation_and_theses/36"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A boundary decay condition, called vanishing to infinite logarithmic order is introduced. A pseudodifferential calculus, extending the b-calculus of Melrose, is proposed based on this modest decay condition. The mapping properties, composition rule, and normal operators are studied. Instead of functional analytic methods, a geometric approach is invoked in pursuing the Fredholm criterion. As an application, a detailed proof of the Atiyah-Patodi-Singer index theorem, including a review of Dirac operators of product type and construction of the heat kernel, is presented.
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