{"id":{"repo_id":"greece","oai_identifier":"oai:10442/1363"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/1363","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"Θεωρία προσέγγισης με νόρμες του Lorentz πάνω σε ομάδες του Lie","abstract":"Study of the motivated certain problems arising from potential operator Δ-A/Z acting on functions which are defined on nilpotent Lie groups. When the heat Kernel PT(N) is defined on a general nilpotent Lie group the estimate depends on the value of T i.e. is different for small and large T, hence the need to introduce the new Lorentz spaces which are development in this thesis. Several interpolation and convolution theorems are proved and the target is the last convolution theorem which contains the known Hardy-Littlewood-Varopoulos theorem for the potential operator acting on nilpotent Lie groups.","abstract_html":"Study of the motivated certain problems arising from potential operator Δ-A/Z acting on functions which are defined on nilpotent Lie groups. When the heat Kernel PT(N) is defined on a general nilpotent Lie group the estimate depends on the value of T i.e. is different for small and large T, hence the need to introduce the new Lorentz spaces which are development in this thesis. Several interpolation and convolution theorems are proved and the target is the last convolution theorem which contains the known Hardy-Littlewood-Varopoulos theorem for the potential operator acting on nilpotent Lie groups.","abstract_has_math":false,"creators":["Τυχόπουλος, Ευάγγελος","Tychopoulos, Evangelos"],"institution":"National Technical University of Athens (NTUA)","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1990,"date_issued":"1990","date_published":"1990","updated_at":"2026-07-24T02:24:52Z","subjects":["Ημιομάδα","Θεωρία προσέγγισης","Νόρμες του Lorentz","Ομάδες Lie","Παρεμβολή","Συνέλιξης","Approximation Theory","Convolution","Interpolation","Lorentz norms","Nilpotent Lie group","Semi group","Φυσικές Επιστήμες","Φυσική","Natural Sciences","Physical Sciences"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1363"],"render_values":[{"text":"10.12681/eadd/1363","href":"https://doi.org/10.12681/eadd/1363","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/1363","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Τυχόπουλος, Ευάγγελος","Tychopoulos, Evangelos"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1990"]},{"key":"dc:publisher","label":"Institution","values":["National Technical University of Athens (NTUA)","Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ)"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Ημιομάδα","Θεωρία προσέγγισης","Νόρμες του Lorentz","Ομάδες Lie","Παρεμβολή","Συνέλιξης","Approximation Theory","Convolution","Interpolation","Lorentz norms","Nilpotent Lie group","Semi group","Φυσικές Επιστήμες","Φυσική","Natural Sciences","Physical Sciences"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["gre"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1363","http://hdl.handle.net/10442/hedi/1363"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Study of the motivated certain problems arising from potential operator Δ-A/Z acting on functions which are defined on nilpotent Lie groups. When the heat Kernel PT(N) is defined on a general nilpotent Lie group the estimate depends on the value of T i.e. is different for small and large T, hence the need to introduce the new Lorentz spaces which are development in this thesis. Several interpolation and convolution theorems are proved and the target is the last convolution theorem which contains the known Hardy-Littlewood-Varopoulos theorem for the potential operator acting on nilpotent Lie groups.","Μελέτη των γενικευμένων χώρων του Lorentz σαν ανάγκη που προκύπτει από την διαφορετική συμπεριφορά του πυρήνα της θερμότητος όταν βρίσκεται κοντά στο 0 και όταν βρίσκεται κοντά στο. Η διαφορετική αυτή συμπεριφορά επιδρά στον τελεστή του δυναμικού όταν αυτός ορίζεται πάνω σε συναρτήσεις οι οποίες με τη σειρά τους είναι ορισμένες πάνω σε μια μηδενοδυναμική ομάδα του Lie. Ανάλυση ορισμένων τοπολογικών ιδιοτήτων των παραπάνω χωρών, δύο παρεμβολικών θεωρημάτων και μιας σειράς από συνελικτικές προτάσεις με αποτέλεσμα το τελευταίο συνελικτικό θεώρημα το οποίο περιέχει το Hardy-Littlewood-Varopoulos θεώρημα."]},{"key":"dc:title","label":"Title","values":["Θεωρία προσέγγισης με νόρμες του Lorentz πάνω σε ομάδες του Lie","Approximation theory with Lorentz norms on Lie groups"]}]}],"canonical_facts":{"dc:creator":["Τυχόπουλος, Ευάγγελος","Tychopoulos, Evangelos"],"dc:date":["1990"],"dc:description":["Study of the motivated certain problems arising from potential operator Δ-A/Z acting on functions which are defined on nilpotent Lie groups. When the heat Kernel PT(N) is defined on a general nilpotent Lie group the estimate depends on the value of T i.e. is different for small and large T, hence the need to introduce the new Lorentz spaces which are development in this thesis. Several interpolation and convolution theorems are proved and the target is the last convolution theorem which contains the known Hardy-Littlewood-Varopoulos theorem for the potential operator acting on nilpotent Lie groups.","Μελέτη των γενικευμένων χώρων του Lorentz σαν ανάγκη που προκύπτει από την διαφορετική συμπεριφορά του πυρήνα της θερμότητος όταν βρίσκεται κοντά στο 0 και όταν βρίσκεται κοντά στο. Η διαφορετική αυτή συμπεριφορά επιδρά στον τελεστή του δυναμικού όταν αυτός ορίζεται πάνω σε συναρτήσεις οι οποίες με τη σειρά τους είναι ορισμένες πάνω σε μια μηδενοδυναμική ομάδα του Lie. Ανάλυση ορισμένων τοπολογικών ιδιοτήτων των παραπάνω χωρών, δύο παρεμβολικών θεωρημάτων και μιας σειράς από συνελικτικές προτάσεις με αποτέλεσμα το τελευταίο συνελικτικό θεώρημα το οποίο περιέχει το Hardy-Littlewood-Varopoulos θεώρημα."],"dc:identifier":["10.12681/eadd/1363","http://hdl.handle.net/10442/hedi/1363"],"dc:language":["gre"],"dc:publisher":["National Technical University of Athens (NTUA)","Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ)"],"dc:subject":["Ημιομάδα","Θεωρία προσέγγισης","Νόρμες του Lorentz","Ομάδες Lie","Παρεμβολή","Συνέλιξης","Approximation Theory","Convolution","Interpolation","Lorentz norms","Nilpotent Lie group","Semi group","Φυσικές Επιστήμες","Φυσική","Natural Sciences","Physical Sciences"],"dc:title":["Θεωρία προσέγγισης με νόρμες του Lorentz πάνω σε ομάδες του Lie","Approximation theory with Lorentz norms on Lie groups"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:24:52Z"}