000119916 001__ 119916
000119916 005__ 20240319081017.0
000119916 0247_ $$2doi$$a10.1007/s00009-022-02155-7
000119916 0248_ $$2sideral$$a130677
000119916 037__ $$aART-2022-130677
000119916 041__ $$aeng
000119916 100__ $$0(orcid)0000-0003-4189-0268$$aMahillo, Alejandro$$uUniversidad de Zaragoza
000119916 245__ $$aCatalan Generating Functions for Generators of Uni-parametric Families of Operators
000119916 260__ $$c2022
000119916 5060_ $$aAccess copy available to the general public$$fUnrestricted
000119916 5203_ $$aIn this paper we study solutions of the quadratic equation AY2−Y+I=0 where A is the generator of a one parameter family of operator (C0-semigroup or cosine functions) on a Banach space X with growth bound w0≤14. In the case of C0-semigroups, we show that a solution, which we call Catalan generating function of A, C(A), is given by the following Bochner integral,
C(A)x:=∫∞0c(t)T(t)xdt,x∈X,
where c is the Catalan kernel,
c(t):=12π∫∞14e−λt4λ−1−−−−−√λdλ,t>0.
Similar (and more complicated) results hold for cosine functions. We study algebraic properties of the Catalan kernel c as an element in Banach algebras L1ω(R+), endowed with the usual convolution product, ∗ and with the cosine convolution product, ∗c. The Hille–Phillips functional calculus allows to transfer these properties to C0-semigroups and cosine functions. In particular, we obtain a spectral mapping theorem for C(A). Finally, we present some examples, applications and conjectures to illustrate our results.
000119916 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E48-20R$$9info:eu-repo/grantAgreement/ES/MCYTS-DGI-FEDER/PID2019-105979GB-I00
000119916 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000119916 590__ $$a1.1$$b2022
000119916 592__ $$a0.531$$b2022
000119916 591__ $$aMATHEMATICS$$b101 / 329 = 0.307$$c2022$$dQ2$$eT1
000119916 593__ $$aMathematics (miscellaneous)$$c2022$$dQ2
000119916 591__ $$aMATHEMATICS, APPLIED$$b161 / 267 = 0.603$$c2022$$dQ3$$eT2
000119916 594__ $$a1.7$$b2022
000119916 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000119916 700__ $$0(orcid)0000-0001-9430-343X$$aMiana, Pedro J.$$uUniversidad de Zaragoza
000119916 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático
000119916 773__ $$g19, 5 (2022), 238 [27 pp.]$$pMediterranean Journal of Mathematics$$tMediterranean Journal of Mathematics$$x1660-5446
000119916 8564_ $$s651847$$uhttps://zaguan.unizar.es/record/119916/files/texto_completo.pdf$$yVersión publicada
000119916 8564_ $$s1006291$$uhttps://zaguan.unizar.es/record/119916/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000119916 909CO $$ooai:zaguan.unizar.es:119916$$particulos$$pdriver
000119916 951__ $$a2024-03-18-15:45:05
000119916 980__ $$aARTICLE