{"id":{"repo_id":"vilnius","oai_identifier":"oai:vu.lt:elaba:1914999"},"canonical_url":"https://search.dev.ndltd.org/etd/vilnius/oai:vu.lt:elaba:1914999","repository":{"repo_id":"vilnius","name":"Vilnius University","base_url":"https://epublications.vu.lt/oai"},"display":{"title":"Logaritminės eilės begalinio indekso nehomogeninis kraštinis Rymano uždavinys sričiai, apribotai begaliniu Dini – Lipšico kontūru /","abstract":"In this work is formulated and studied boundary Riemann problem of logarithmic order α≥1 for the space bounded by the infinite Dini – Lipschitz contour. In this paper is used asymptotics of Cauchy type integrals with a logarithmic density. Basically differ functions Фα(z) and Фα*(z). In the first integral lnαt is contour value of the analytical function lnαz and for Cauchy-type integral Фα(z) is obtained polynomial asymptotic formula. Function Фα*(z) associated with the canonical function X(z) obtained in asymptotic formula is the only one, the fastest growing member, when z→∞. The information about the change of the Фα*(z) is insufficient considering inhomogeneous problem. It is necessary to use the Dini – Lipschitz contour. Let L΄ be Dini – Lipschitz contour of q>α order, it is proved that the function ηα(t) is continuous and bounded in contour L΄ points, and zeros of entire function F0(z) are arranged on the negative semi-axis of the real axis. Being the before mentioned contour, it was proved that a separate inhomogeneous target solution is bounded. In this work is obtained the general solution of formulated task of bounded functions in class BL.","abstract_html":"In this work is formulated and studied boundary Riemann problem of logarithmic order α≥1 for the space bounded by the infinite Dini – Lipschitz contour. In this paper is used asymptotics of Cauchy type integrals with a logarithmic density. Basically differ functions Фα(z) and Фα*(z). In the first integral lnαt is contour value of the analytical function lnαz and for Cauchy-type integral Фα(z) is obtained polynomial asymptotic formula. Function Фα*(z) associated with the canonical function X(z) obtained in asymptotic formula is the only one, the fastest growing member, when z→∞. The information about the change of the Фα*(z) is insufficient considering inhomogeneous problem. It is necessary to use the Dini – Lipschitz contour. Let L΄ be Dini – Lipschitz contour of q>α order, it is proved that the function ηα(t) is continuous and bounded in contour L΄ points, and zeros of entire function F0(z) are arranged on the negative semi-axis of the real axis. Being the before mentioned contour, it was proved that a separate inhomogeneous target solution is bounded. In this work is obtained the general solution of formulated task of bounded functions in class BL.","abstract_has_math":false,"creators":["Spetylaitė, Jurga,"],"institution":"Institutional Repository of Vilnius University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Alekna, Petras"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009","date_published":"2009","updated_at":"2026-07-24T05:55:31Z","subjects":["contour ; logaruthmic ; density ; index"],"languages":["lit"],"rights":["info:eu-repo/semantics/openAccess"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://repository.vu.lt/VU:ELABAETD1914999&prefLang=en_US","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Alekna, Petras"]},{"key":"dc:creator","label":"Author","values":["Spetylaitė, Jurga,"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2009"]},{"key":"dc:publisher","label":"Institution","values":["Institutional Repository of Vilnius University"]},{"key":"dc:relation","label":"Dc Relation","values":["https://epublications.vu.lt/object/elaba:1914999/1914999.pdf"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/masterThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["contour ; logaruthmic ; density ; index"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["lit"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://repository.vu.lt/VU:ELABAETD1914999&prefLang=en_US"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this work is formulated and studied boundary Riemann problem of logarithmic order α≥1 for the space bounded by the infinite Dini – Lipschitz contour. In this paper is used asymptotics of Cauchy type integrals with a logarithmic density. Basically differ functions Фα(z) and Фα*(z). In the first integral lnαt is contour value of the analytical function lnαz and for Cauchy-type integral Фα(z) is obtained polynomial asymptotic formula. Function Фα*(z) associated with the canonical function X(z) obtained in asymptotic formula is the only one, the fastest growing member, when z→∞. The information about the change of the Фα*(z) is insufficient considering inhomogeneous problem. It is necessary to use the Dini – Lipschitz contour. Let L΄ be Dini – Lipschitz contour of q>α order, it is proved that the function ηα(t) is continuous and bounded in contour L΄ points, and zeros of entire function F0(z) are arranged on the negative semi-axis of the real axis. Being the before mentioned contour, it was proved that a separate inhomogeneous target solution is bounded. In this work is obtained the general solution of formulated task of bounded functions in class BL."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Logaritminės eilės begalinio indekso nehomogeninis kraštinis Rymano uždavinys sričiai, apribotai begaliniu Dini – Lipšico kontūru /","The inhomogeneous Riemann boundary - value problem with infinite index of the logarithmic order for the region limited by the infinity Dini - Lipschitz contour."]}]}],"canonical_facts":{"dc:contributor":["Alekna, Petras"],"dc:creator":["Spetylaitė, Jurga,"],"dc:date":["2009"],"dc:description":["In this work is formulated and studied boundary Riemann problem of logarithmic order α≥1 for the space bounded by the infinite Dini – Lipschitz contour. In this paper is used asymptotics of Cauchy type integrals with a logarithmic density. Basically differ functions Фα(z) and Фα*(z). In the first integral lnαt is contour value of the analytical function lnαz and for Cauchy-type integral Фα(z) is obtained polynomial asymptotic formula. Function Фα*(z) associated with the canonical function X(z) obtained in asymptotic formula is the only one, the fastest growing member, when z→∞. The information about the change of the Фα*(z) is insufficient considering inhomogeneous problem. It is necessary to use the Dini – Lipschitz contour. Let L΄ be Dini – Lipschitz contour of q>α order, it is proved that the function ηα(t) is continuous and bounded in contour L΄ points, and zeros of entire function F0(z) are arranged on the negative semi-axis of the real axis. Being the before mentioned contour, it was proved that a separate inhomogeneous target solution is bounded. In this work is obtained the general solution of formulated task of bounded functions in class BL."],"dc:format":["application/pdf"],"dc:identifier":["https://repository.vu.lt/VU:ELABAETD1914999&prefLang=en_US"],"dc:language":["lit"],"dc:publisher":["Institutional Repository of Vilnius University"],"dc:relation":["https://epublications.vu.lt/object/elaba:1914999/1914999.pdf"],"dc:rights":["info:eu-repo/semantics/openAccess"],"dc:subject":["contour ; logaruthmic ; density ; index"],"dc:title":["Logaritminės eilės begalinio indekso nehomogeninis kraštinis Rymano uždavinys sričiai, apribotai begaliniu Dini – Lipšico kontūru /","The inhomogeneous Riemann boundary - value problem with infinite index of the logarithmic order for the region limited by the infinity Dini - Lipschitz contour."],"dc:type":["info:eu-repo/semantics/masterThesis"]},"updated_at":"2026-07-24T05:55:31Z"}