{"id":{"repo_id":"rice","oai_identifier":"oai:repository.rice.edu:1911/18366"},"canonical_url":"https://search.dev.ndltd.org/etd/rice/oai:repository.rice.edu:1911/18366","repository":{"repo_id":"rice","name":"Rice University","base_url":"https://repository.rice.edu/server/oai/request"},"display":{"title":"Invariant functionals","abstract":"The study of continuous groups of transformations in function space was begun by G. Kowalewski in 1911. Vessiot considered the conditions under which r parameter Volterra transformations form a group. L. L. Dines considered projective transformations in function space continuing Kowalewski's work. I. A. Barnett gave a few examples of functionals invariant under one-parameter continuous groups of transformations in the space of continuous functions. The systematic study of functionals invariant under continuous groups of transformations in function space, and also the study of functionals involving derivatives of functions and invariant under groups of transformations in function space have not been considered previously, so far as the writer has been able to ascertain. Consequently the author commences the study of the latter functionals, i.e., functionals involving derivatives of functions (and as a special case, integro-differential equations), that are invariant under a Volterra one parameter group of continuous transformations, a problem allied to the calculus of variations.","abstract_html":"The study of continuous groups of transformations in function space was begun by G. Kowalewski in 1911. Vessiot considered the conditions under which r parameter Volterra transformations form a group. L. L. Dines considered projective transformations in function space continuing Kowalewski's work. I. A. Barnett gave a few examples of functionals invariant under one-parameter continuous groups of transformations in the space of continuous functions. The systematic study of functionals invariant under continuous groups of transformations in function space, and also the study of functionals involving derivatives of functions and invariant under groups of transformations in function space have not been considered previously, so far as the writer has been able to ascertain. Consequently the author commences the study of the latter functionals, i.e., functionals involving derivatives of functions (and as a special case, integro-differential equations), that are invariant under a Volterra one parameter group of continuous transformations, a problem allied to the calculus of variations.","abstract_has_math":false,"creators":["Michal, Aristotle D."],"institution":"Rice University","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Natural Sciences","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1924,"date_issued":"1924","date_published":"1924","updated_at":"2026-07-24T04:10:17Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1911/18366","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Michal, Aristotle D."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2007-08-21T01:04:57Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2007-08-21T01:04:57Z"]},{"key":"dc:date.issued","label":"Date","values":["1924"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Natural Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Rice University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright is held by the author, unless otherwise indicated. 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The systematic study of functionals invariant under continuous groups of transformations in function space, and also the study of functionals involving derivatives of functions and invariant under groups of transformations in function space have not been considered previously, so far as the writer has been able to ascertain. Consequently the author commences the study of the latter functionals, i.e., functionals involving derivatives of functions (and as a special case, integro-differential equations), that are invariant under a Volterra one parameter group of continuous transformations, a problem allied to the calculus of variations."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Invariant functionals"]}]}],"canonical_facts":{"dc:creator":["Michal, Aristotle D."],"dc:date.accessioned":["2007-08-21T01:04:57Z"],"dc:date.available":["2007-08-21T01:04:57Z"],"dc:date.issued":["1924"],"dc:description.abstract":["The study of continuous groups of transformations in function space was begun by G. Kowalewski in 1911. Vessiot considered the conditions under which r parameter Volterra transformations form a group. L. L. Dines considered projective transformations in function space continuing Kowalewski's work. I. A. Barnett gave a few examples of functionals invariant under one-parameter continuous groups of transformations in the space of continuous functions. The systematic study of functionals invariant under continuous groups of transformations in function space, and also the study of functionals involving derivatives of functions and invariant under groups of transformations in function space have not been considered previously, so far as the writer has been able to ascertain. Consequently the author commences the study of the latter functionals, i.e., functionals involving derivatives of functions (and as a special case, integro-differential equations), that are invariant under a Volterra one parameter group of continuous transformations, a problem allied to the calculus of variations."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/1911/18366"],"dc:language.iso":["eng"],"dc:rights":["Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder."],"dc:subject":["Mathematics"],"dc:title":["Invariant functionals"],"dc:type":["Thesis"],"thesis:degree_discipline":["Natural Sciences"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["Rice University"]},"updated_at":"2026-07-24T04:10:17Z"}