LEADER 03323nam 2200613 450 001 9910682559803321 005 20231009162458.0 010 $a3-031-23676-9 024 7 $a10.1007/978-3-031-23676-1 035 $a(MiAaPQ)EBC7214768 035 $a(Au-PeEL)EBL7214768 035 $a(CKB)26270992400041 035 $a(DE-He213)978-3-031-23676-1 035 $a(PPN)269094822 035 $a(EXLCZ)9926270992400041 100 $a20230601d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometry of the Unit Sphere in Polynomial Spaces /$fJesu?s Ferrer [and five others] 205 $aFirst edition. 210 1$aCham, Switzerland :$cSpringer, Springer Nature Switzerland AG,$d[2022] 210 4$d©2022 215 $a1 online resource (140 pages) 225 1 $aSpringerBriefs in Mathematics Series 311 08$aPrint version: Ferrer, Jesús Geometry of the Unit Sphere in Polynomial Spaces Cham : Springer International Publishing AG,c2023 9783031236754 320 $aIncludes bibliographical references. 327 $aChapter. 1. Introduction -- Chapter. 2. Polynomials of degree -- Chapter. 3. Spaces of trinomials -- Chapter. 4. Polynomials on nonsymmetric convex bodies -- Chapter. 5. Sequence Banach spaces -- Chapter. 6. Polynomials with the hexagonal and octagonal norms -- Chapter. 7. Hilbert spaces -- Chapter. 8. Banach spaces -- Chapter. 9. Applications. 330 $aThis brief presents a global perspective on the geometry of spaces of polynomials. Its particular focus is on polynomial spaces of dimension 3, providing, in that case, a graphical representation of the unit ball. Also, the extreme points in the unit ball of several polynomial spaces are characterized. Finally, a number of applications to obtain sharp classical polynomial inequalities are presented. The study performed is the first ever complete account on the geometry of the unit ball of polynomial spaces. Nowadays there are hundreds of research papers on this topic and our work gathers the state of the art of the main and/or relevant results up to now. This book is intended for a broad audience, including undergraduate and graduate students, junior and senior researchers and it also serves as a source book for consultation. In addition to that, we made this work visually attractive by including in it over 50 original figures in order to help in the understanding of all the results and techniques included in the book. 410 0$aSpringerBriefs in mathematics. 606 $aFunctional analysis 606 $aGeometry, Algebraic 606 $aPolynomials 606 $aAnàlisi funcional$2thub 606 $aGeometria algebraica$2thub 606 $aPolinomis$2thub 608 $aLlibres electrònics$2thub 615 0$aFunctional analysis. 615 0$aGeometry, Algebraic. 615 0$aPolynomials. 615 7$aAnàlisi funcional 615 7$aGeometria algebraica 615 7$aPolinomis 676 $a515.7 700 $aFerrer$b Jesu?s$00 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910682559803321 996 $aGeometry of the Unit Sphere in Polynomial Spaces$93383238 997 $aUNINA