FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3048658462> ?p ?o ?g. }

• W3048658462 abstract "We prove the converse to a result of Karlin [Trans. AMS 1964], and also strengthen his result and two results of Schoenberg [Ann. of Math. 1955]. One of the latter results concerns zeros of Laplace transforms of multiply positive functions. The other results study which powers $alpha$ of two specific kernels are totally non-negative of order $pgeq 2$ (denoted TN$_p$); both authors showed this happens for $alphageq p-2$, and Schoenberg proved that it does not for $alpha p-2$, and is not TN$_p$ for every $alphain(0,p-2)setminusmathbb{Z}$. In particular, these results reveal a 'critical exponent' phenomenon in total positivity. (This exponent $(p-2)$ was first discovered by FitzGerald-Horn in [JMAA 1977] for positivity.) We also provide a characterization for Polya frequency functions of order $p geq 3$, following Schoenberg's result for $p=2$ in [J. Analyse Math. 1951]. Our proofs are self-contained, with three exceptions. We further classify the powers preserving all TN$_p$ Hankel kernels on intervals, and isolate individual kernels encoding these powers. We then transfer results on preservers by Polya-Szego (1925), Loewner/Horn (1969), and Khare-Tao (2017), from positive semidefinite matrices to Hankel TN$_p$ kernels. An additional application of the proofs is to construct individual matrices that encode the Loewner convex powers. This complements Jain's results (2020) for Loewner positivity, which we strengthen to total positivity, with self-contained proofs. Remarkably, these (strengthened) results of Jain, those of Schoenberg and Karlin, the latter's converse, and the aforementioned individual Hankel kernels all arise from a single symmetric rank-two kernel and its powers: $max(1+xy,0)$." @default.
• W3048658462 created "2020-08-18" @default.
• W3048658462 creator A5059899589 @default.
• W3048658462 date "2020-08-12" @default.
• W3048658462 modified "2023-09-27" @default.
• W3048658462 title "Critical exponents for total positivity, individual kernel encoders, and the Jain-Karlin-Schoenberg kernel." @default.
• W3048658462 cites W1678167890 @default.
• W3048658462 cites W1861968797 @default.
• W3048658462 cites W1965305383 @default.
• W3048658462 cites W1972115506 @default.
• W3048658462 cites W1987225390 @default.
• W3048658462 cites W1995574858 @default.
• W3048658462 cites W1998041147 @default.
• W3048658462 cites W2007154098 @default.
• W3048658462 cites W2007457540 @default.
• W3048658462 cites W2017943326 @default.
• W3048658462 cites W2021331271 @default.
• W3048658462 cites W2021813574 @default.
• W3048658462 cites W2032382375 @default.
• W3048658462 cites W2038869014 @default.
• W3048658462 cites W2052945071 @default.
• W3048658462 cites W2062762227 @default.
• W3048658462 cites W2066913327 @default.
• W3048658462 cites W2076977679 @default.
• W3048658462 cites W2139999468 @default.
• W3048658462 cites W2140118638 @default.
• W3048658462 cites W2324388691 @default.
• W3048658462 cites W2329983323 @default.
• W3048658462 cites W2508429878 @default.
• W3048658462 cites W2515040851 @default.
• W3048658462 cites W2559961335 @default.
• W3048658462 cites W2749223062 @default.
• W3048658462 cites W2788355224 @default.
• W3048658462 cites W2963078539 @default.
• W3048658462 cites W2964272847 @default.
• W3048658462 cites W3024301360 @default.
• W3048658462 cites W3028167933 @default.
• W3048658462 cites W3037514954 @default.
• W3048658462 cites W3102146249 @default.
• W3048658462 cites W568790798 @default.
• W3048658462 cites W792989641 @default.
• W3048658462 hasPublicationYear "2020" @default.
• W3048658462 type Work @default.
• W3048658462 sameAs 3048658462 @default.
• W3048658462 citedByCount "1" @default.
• W3048658462 countsByYear W30486584622021 @default.
• W3048658462 crossrefType "posted-content" @default.
• W3048658462 hasAuthorship W3048658462A5059899589 @default.
• W3048658462 hasConcept C10138342 @default.
• W3048658462 hasConcept C108710211 @default.
• W3048658462 hasConcept C114614502 @default.
• W3048658462 hasConcept C118615104 @default.
• W3048658462 hasConcept C134306372 @default.
• W3048658462 hasConcept C138885662 @default.
• W3048658462 hasConcept C162324750 @default.
• W3048658462 hasConcept C182306322 @default.
• W3048658462 hasConcept C2524010 @default.
• W3048658462 hasConcept C2780388253 @default.
• W3048658462 hasConcept C33923547 @default.
• W3048658462 hasConcept C41895202 @default.
• W3048658462 hasConcept C74193536 @default.
• W3048658462 hasConcept C97937538 @default.
• W3048658462 hasConceptScore W3048658462C10138342 @default.
• W3048658462 hasConceptScore W3048658462C108710211 @default.
• W3048658462 hasConceptScore W3048658462C114614502 @default.
• W3048658462 hasConceptScore W3048658462C118615104 @default.
• W3048658462 hasConceptScore W3048658462C134306372 @default.
• W3048658462 hasConceptScore W3048658462C138885662 @default.
• W3048658462 hasConceptScore W3048658462C162324750 @default.
• W3048658462 hasConceptScore W3048658462C182306322 @default.
• W3048658462 hasConceptScore W3048658462C2524010 @default.
• W3048658462 hasConceptScore W3048658462C2780388253 @default.
• W3048658462 hasConceptScore W3048658462C33923547 @default.
• W3048658462 hasConceptScore W3048658462C41895202 @default.
• W3048658462 hasConceptScore W3048658462C74193536 @default.
• W3048658462 hasConceptScore W3048658462C97937538 @default.
• W3048658462 hasLocation W30486584621 @default.
• W3048658462 hasOpenAccess W3048658462 @default.
• W3048658462 hasPrimaryLocation W30486584621 @default.
• W3048658462 hasRelatedWork W1656663720 @default.
• W3048658462 hasRelatedWork W1997553035 @default.
• W3048658462 hasRelatedWork W2041874120 @default.
• W3048658462 hasRelatedWork W2148143783 @default.
• W3048658462 hasRelatedWork W2560919991 @default.
• W3048658462 hasRelatedWork W2890653589 @default.
• W3048658462 hasRelatedWork W2896269717 @default.
• W3048658462 hasRelatedWork W2953109492 @default.
• W3048658462 hasRelatedWork W2963272700 @default.
• W3048658462 hasRelatedWork W3083596116 @default.
• W3048658462 hasRelatedWork W3088032824 @default.
• W3048658462 hasRelatedWork W3101233038 @default.
• W3048658462 hasRelatedWork W3105580025 @default.
• W3048658462 hasRelatedWork W3157155820 @default.
• W3048658462 hasRelatedWork W3158300389 @default.
• W3048658462 hasRelatedWork W3179423538 @default.
• W3048658462 hasRelatedWork W3196702835 @default.
• W3048658462 hasRelatedWork W3207517228 @default.
• W3048658462 hasRelatedWork W3208589802 @default.
• W3048658462 hasRelatedWork W1838014566 @default.
• W3048658462 isParatext "false" @default.

• next