We study the strongest concavity property preserved by the Dirichlet heat flow, characterizing log-concavity in this connection. To this aim, we also review and investigate the notion of F-concavity, which largely generalizes the usual concavity. As side results, by the use of the notions of closedness under positive scalar multiplication and closedness under positive exponentiation, we characterize power concavity and power log-concavity among nontrivial F-concavities, respectively (showing in particular that log-concavity is the only F-concavity which is closed both under positive scalar multiplication and positive exponentiation).

New characterizations of log-concavity via Dirichlet heat flow / Ishige K.; Salani P.; Takatsu A.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 201:(2022), pp. 1531-1552. [10.1007/s10231-021-01168-5]

New characterizations of log-concavity via Dirichlet heat flow

Ishige K.;Salani P.
;
Takatsu A.
2022

Abstract

We study the strongest concavity property preserved by the Dirichlet heat flow, characterizing log-concavity in this connection. To this aim, we also review and investigate the notion of F-concavity, which largely generalizes the usual concavity. As side results, by the use of the notions of closedness under positive scalar multiplication and closedness under positive exponentiation, we characterize power concavity and power log-concavity among nontrivial F-concavities, respectively (showing in particular that log-concavity is the only F-concavity which is closed both under positive scalar multiplication and positive exponentiation).
2022
201
1531
1552
Ishige K.; Salani P.; Takatsu A.
File in questo prodotto:
File Dimensione Formato  
Pubblicato.pdf

Accesso chiuso

Descrizione: pdf editoriale pubblicato online
Tipologia: Pdf editoriale (Version of record)
Licenza: Tutti i diritti riservati
Dimensione 2.25 MB
Formato Adobe PDF
2.25 MB Adobe PDF   Richiedi una copia
2004.13381.pdf

accesso aperto

Descrizione: Preprint dell'autore
Tipologia: Altro
Licenza: Open Access
Dimensione 234.32 kB
Formato Adobe PDF
234.32 kB Adobe PDF

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1253716
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 2
social impact