{"id":{"repo_id":"greece","oai_identifier":"oai:10442/1179"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/1179","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"ΜΕΛΕΤΗ ΤΩΝ ΡΙΖΩΝ ΜΙΚΤΩΝ ΣΥΝΑΡΤΗΣΕΩΝ BESSEL","abstract":"WE STUDY THE EXISTENCE OR NOT OF THE COMPLEX AND REAL ZEROS OF MIXED BESSEL FUNCTIONS, MV(Z)=F(Z)JV(Z)+G(Z)JV'(Z), OF FIRST KIND AND ORDER V (IN GENERAL COMPLEX). THE MULTIPLICITY OF THE ZEROS OF THE DERIVATIVES OF BESSEL FUNCTIONS JV(S)(Z), S=1,2,3,4 IS ALSO EXAMINED. FOR THE FUNCTION JV''(Z), WHICH IS A SPECIAL CASE OF THE FUNCTION MV(Z), WE GIVE UPPER AND LOWER BOUNDS FOR THE FIRST POSITIVE ZERO OF IT. WE ALSO OBTAIN THE DIFFERENTIAL EQUATION WHICH SATISFY THE ZEROS OF THE FUNCTION MV(Z) AND WE STUDY THE MONOTONICITY OF THE POSITIVE ZEROS OF THAT FUNCTION, AS WELL AS THE POSITIVE FUNCTION R(V) OF THE IMAGINARY ZEROS +IR(V) OF THE FUNCTION JV'(Z).","abstract_html":"WE STUDY THE EXISTENCE OR NOT OF THE COMPLEX AND REAL ZEROS OF MIXED BESSEL FUNCTIONS, MV(Z)=F(Z)JV(Z)+G(Z)JV'(Z), OF FIRST KIND AND ORDER V (IN GENERAL COMPLEX). THE MULTIPLICITY OF THE ZEROS OF THE DERIVATIVES OF BESSEL FUNCTIONS JV(S)(Z), S=1,2,3,4 IS ALSO EXAMINED. FOR THE FUNCTION JV''(Z), WHICH IS A SPECIAL CASE OF THE FUNCTION MV(Z), WE GIVE UPPER AND LOWER BOUNDS FOR THE FIRST POSITIVE ZERO OF IT. WE ALSO OBTAIN THE DIFFERENTIAL EQUATION WHICH SATISFY THE ZEROS OF THE FUNCTION MV(Z) AND WE STUDY THE MONOTONICITY OF THE POSITIVE ZEROS OF THAT FUNCTION, AS WELL AS THE POSITIVE FUNCTION R(V) OF THE IMAGINARY ZEROS +IR(V) OF THE FUNCTION JV'(Z).","abstract_has_math":false,"creators":["Kokologiannaki, Chrysi","Κοκολογιαννάκη-Κωνσταντοπούλου, Χρυσή"],"institution":"University of Patras","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1989,"date_issued":"1989","date_published":"1989","updated_at":"2026-07-24T02:24:46Z","subjects":["ΑΥΤΟΣΥΖΥΓΕΙΣ, ΣΥΜΠΑΓΕΙΣ ΤΕΛΕΣΤΕΣ","Μαθηματικά","ΜΙΚΤΕΣ ΣΥΝΑΡΤΗΣΕΙΣ BESSEL","Ρίζες","ΣΥΝΑΡΤΗΣΕΙΣ, ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ","FUNCTIONS, DIFFERENTIAL EQUATIONS","Mathematics","MIXED BESSEL FUNCTIONS","SELFADJOINT, COMPACT OPERATORS","Zeros","Φυσικές Επιστήμες","Natural Sciences"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1179"],"render_values":[{"text":"10.12681/eadd/1179","href":"https://doi.org/10.12681/eadd/1179","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/1179","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Kokologiannaki, Chrysi","Κοκολογιαννάκη-Κωνσταντοπούλου, Χρυσή"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1989"]},{"key":"dc:publisher","label":"Institution","values":["University of Patras","Πανεπιστήμιο Πατρών"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ΑΥΤΟΣΥΖΥΓΕΙΣ, ΣΥΜΠΑΓΕΙΣ ΤΕΛΕΣΤΕΣ","Μαθηματικά","ΜΙΚΤΕΣ ΣΥΝΑΡΤΗΣΕΙΣ BESSEL","Ρίζες","ΣΥΝΑΡΤΗΣΕΙΣ, ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ","FUNCTIONS, DIFFERENTIAL EQUATIONS","Mathematics","MIXED BESSEL FUNCTIONS","SELFADJOINT, COMPACT OPERATORS","Zeros","Φυσικές Επιστήμες","Natural 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/1179","http://hdl.handle.net/10442/hedi/1179"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["WE STUDY THE EXISTENCE OR NOT OF THE COMPLEX AND REAL ZEROS OF MIXED BESSEL FUNCTIONS, MV(Z)=F(Z)JV(Z)+G(Z)JV'(Z), OF FIRST KIND AND ORDER V (IN GENERAL COMPLEX). THE MULTIPLICITY OF THE ZEROS OF THE DERIVATIVES OF BESSEL FUNCTIONS JV(S)(Z), S=1,2,3,4 IS ALSO EXAMINED. FOR THE FUNCTION JV''(Z), WHICH IS A SPECIAL CASE OF THE FUNCTION MV(Z), WE GIVE UPPER AND LOWER BOUNDS FOR THE FIRST POSITIVE ZERO OF IT. WE ALSO OBTAIN THE DIFFERENTIAL EQUATION WHICH SATISFY THE ZEROS OF THE FUNCTION MV(Z) AND WE STUDY THE MONOTONICITY OF THE POSITIVE ZEROS OF THAT FUNCTION, AS WELL AS THE POSITIVE FUNCTION R(V) OF THE IMAGINARY ZEROS +IR(V) OF THE FUNCTION JV'(Z).","ΜΕΛΕΤΑΤΑΙ Η ΥΠΑΡΞΗ 'Η ΜΗ ΤΩΝ ΜΙΓΑΔΙΚΩΝ ΚΑΙ ΠΡΑΓΜΑΤΙΚΩΝ ΡΙΖΩΝ ΤΩΝ ΜΙΚΤΩΝ ΣΥΝΑΡΤΗΣΕΩΝ BESSEL MV(Z)=F(Z)JV(Z)+G(Z)JV'(Z), ΠΡΩΤΟΥ ΕΙΔΟΥΣ ΚΑΙ ΤΑΞΗΣ V (ΕΝ ΓΕΝΕΙ ΜΙΓΑΔΙΚΟΣ). ΕΠΙΣΗΣ, Η ΠΟΛΛΑΠΛΟΤΗΤΑ ΤΩΝ ΡΙΖΩΝ ΤΩΝ ΠΑΡΑΓΩΓΩΝ ΤΩΝ ΣΥΝΑΡΤΗΣΕΩΝ BESSEL JV(S)(Z), S=1,2,3,4. ΓΙΝΕΤΑΙ ΜΕΛΕΤΗ ΤΩΝ ΡΙΖΩΝ ΤΗΣ ΣΥΝΑΡΤΗΣΗΣ (ΒΖ2+Α)JV(Z)+ZJV'(Z) ΚΑΙ ΔΙΝΟΝΤΑΙ ΑΝΩ ΚΑΙ ΚΑΤΩ ΦΡΑΓΜΑΤΑ ΓΙΑ ΤΗΝ ΠΡΩΤΗ ΘΕΤΙΚΗ ΡΙΖΑ ΤΗΣ ΣΥΝΑΡΤΗΣΗΣ HJV''(Z), Η ΟΠΟΙΑ ΠΡΟΚΥΠΤΕΙ ΑΠΟ ΤΗΝ ΑΝΩΤΕΡΩ, ΓΙΑ Β=1 ΚΑΙ Α=-V2. ΕΠΙΣΗΣ, ΔΙΝΕΤΑΙΗ ΔΙΑΦΟΡΙΚΗ ΕΞΙΣΩΣΗ ΠΟΥ ΙΚΑΝΟΠΟΙΟΥΝ ΟΙ ΡΙΖΕΣ ΤΗΣ ΣΥΝΑΡΤΗΣΗΣ MV(Z) ΚΑΙ ΜΕΛΕΤΑΤΑΙ Η ΜΟΝΟΤΟΝΙΑ ΤΩΝ ΘΕΤΙΚΩΝ ΡΙΖΩΝ ΑΥΤΗΣ ΚΑΘΩΣ ΚΑΙ ΤΗΣ ΘΕΤΙΚΗΣ ΣΥΝΑΡΤΗΣΗΣ R(V) ΤΩΝΦΑΝΤΑΣΤΙΚΩΝ ΡΙΖΩΝ + IR(V) ΤΗΣ ΣΥΝΑΡΤΗΣΗΣ JV'(Z)."]},{"key":"dc:title","label":"Title","values":["ΜΕΛΕΤΗ ΤΩΝ ΡΙΖΩΝ ΜΙΚΤΩΝ ΣΥΝΑΡΤΗΣΕΩΝ BESSEL","STUDY OF THE ZEROS OF MIXED BESSEL FUNCTIONS"]}]}],"canonical_facts":{"dc:creator":["Kokologiannaki, Chrysi","Κοκολογιαννάκη-Κωνσταντοπούλου, Χρυσή"],"dc:date":["1989"],"dc:description":["WE STUDY THE EXISTENCE OR NOT OF THE COMPLEX AND REAL ZEROS OF MIXED BESSEL FUNCTIONS, MV(Z)=F(Z)JV(Z)+G(Z)JV'(Z), OF FIRST KIND AND ORDER V (IN GENERAL COMPLEX). THE MULTIPLICITY OF THE ZEROS OF THE DERIVATIVES OF BESSEL FUNCTIONS JV(S)(Z), S=1,2,3,4 IS ALSO EXAMINED. FOR THE FUNCTION JV''(Z), WHICH IS A SPECIAL CASE OF THE FUNCTION MV(Z), WE GIVE UPPER AND LOWER BOUNDS FOR THE FIRST POSITIVE ZERO OF IT. WE ALSO OBTAIN THE DIFFERENTIAL EQUATION WHICH SATISFY THE ZEROS OF THE FUNCTION MV(Z) AND WE STUDY THE MONOTONICITY OF THE POSITIVE ZEROS OF THAT FUNCTION, AS WELL AS THE POSITIVE FUNCTION R(V) OF THE IMAGINARY ZEROS +IR(V) OF THE FUNCTION JV'(Z).","ΜΕΛΕΤΑΤΑΙ Η ΥΠΑΡΞΗ 'Η ΜΗ ΤΩΝ ΜΙΓΑΔΙΚΩΝ ΚΑΙ ΠΡΑΓΜΑΤΙΚΩΝ ΡΙΖΩΝ ΤΩΝ ΜΙΚΤΩΝ ΣΥΝΑΡΤΗΣΕΩΝ BESSEL MV(Z)=F(Z)JV(Z)+G(Z)JV'(Z), ΠΡΩΤΟΥ ΕΙΔΟΥΣ ΚΑΙ ΤΑΞΗΣ V (ΕΝ ΓΕΝΕΙ ΜΙΓΑΔΙΚΟΣ). ΕΠΙΣΗΣ, Η ΠΟΛΛΑΠΛΟΤΗΤΑ ΤΩΝ ΡΙΖΩΝ ΤΩΝ ΠΑΡΑΓΩΓΩΝ ΤΩΝ ΣΥΝΑΡΤΗΣΕΩΝ BESSEL JV(S)(Z), S=1,2,3,4. ΓΙΝΕΤΑΙ ΜΕΛΕΤΗ ΤΩΝ ΡΙΖΩΝ ΤΗΣ ΣΥΝΑΡΤΗΣΗΣ (ΒΖ2+Α)JV(Z)+ZJV'(Z) ΚΑΙ ΔΙΝΟΝΤΑΙ ΑΝΩ ΚΑΙ ΚΑΤΩ ΦΡΑΓΜΑΤΑ ΓΙΑ ΤΗΝ ΠΡΩΤΗ ΘΕΤΙΚΗ ΡΙΖΑ ΤΗΣ ΣΥΝΑΡΤΗΣΗΣ HJV''(Z), Η ΟΠΟΙΑ ΠΡΟΚΥΠΤΕΙ ΑΠΟ ΤΗΝ ΑΝΩΤΕΡΩ, ΓΙΑ Β=1 ΚΑΙ Α=-V2. ΕΠΙΣΗΣ, ΔΙΝΕΤΑΙΗ ΔΙΑΦΟΡΙΚΗ ΕΞΙΣΩΣΗ ΠΟΥ ΙΚΑΝΟΠΟΙΟΥΝ ΟΙ ΡΙΖΕΣ ΤΗΣ ΣΥΝΑΡΤΗΣΗΣ MV(Z) ΚΑΙ ΜΕΛΕΤΑΤΑΙ Η ΜΟΝΟΤΟΝΙΑ ΤΩΝ ΘΕΤΙΚΩΝ ΡΙΖΩΝ ΑΥΤΗΣ ΚΑΘΩΣ ΚΑΙ ΤΗΣ ΘΕΤΙΚΗΣ ΣΥΝΑΡΤΗΣΗΣ R(V) ΤΩΝΦΑΝΤΑΣΤΙΚΩΝ ΡΙΖΩΝ + IR(V) ΤΗΣ ΣΥΝΑΡΤΗΣΗΣ JV'(Z)."],"dc:identifier":["10.12681/eadd/1179","http://hdl.handle.net/10442/hedi/1179"],"dc:language":["gre"],"dc:publisher":["University of Patras","Πανεπιστήμιο Πατρών"],"dc:subject":["ΑΥΤΟΣΥΖΥΓΕΙΣ, ΣΥΜΠΑΓΕΙΣ ΤΕΛΕΣΤΕΣ","Μαθηματικά","ΜΙΚΤΕΣ ΣΥΝΑΡΤΗΣΕΙΣ BESSEL","Ρίζες","ΣΥΝΑΡΤΗΣΕΙΣ, ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ","FUNCTIONS, DIFFERENTIAL EQUATIONS","Mathematics","MIXED BESSEL FUNCTIONS","SELFADJOINT, COMPACT OPERATORS","Zeros","Φυσικές Επιστήμες","Natural Sciences"],"dc:title":["ΜΕΛΕΤΗ ΤΩΝ ΡΙΖΩΝ ΜΙΚΤΩΝ ΣΥΝΑΡΤΗΣΕΩΝ BESSEL","STUDY OF THE ZEROS OF MIXED BESSEL FUNCTIONS"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:24:46Z"}