References

  1. Aron R.M., Klimek M. Supremum norms for quadratic polynomials. Arch. Math. (Basel) 2001, 76 (1), 73-80. doi: 10.1007/s000130050544
  2. Cavalcante W., Pellegrino D. Geometry of the closed unit ball of the space of bilinear forms on $\ell_{\infty}^2$. arXiv: 1603.01535v2.
  3. Choi Y.S., Kim S.G., Ki H. Extreme Polynomials and Multilinear Forms on $l_1$. J. Math. Anal. Appl. 1998, 228 (2), 467-482. doi: 10.1006/jmaa.1998.6161
  4. Choi Y.S., Kim S.G. The unit ball of $\mathcal{P}(^2l_2^2)$. Arch. Math. (Basel) 1998, 71 (6), 472-480. doi: 10.1007/s000130050292
  5. Choi Y.S., Kim S.G. Extreme polynomials on $c_0$. Indian J. Pure Appl. Math. 1998, 29 (10), 983-989.
  6. Choi Y.S., Kim S.G. Smooth points of the unit ball of the space $\mathcal{P}(^2l_1)$. Results Math. 1999, 36, 26-33. doi: 10.1007/BF03322099
  7. Choi Y.S., Kim S.G. Exposed points of the unit balls of the spaces $\mathcal{P}(^2l_p^2)~(p=1, 2,\infty)$. Indian J. Pure Appl. Math. 2004, 35 (1), 37-41.
  8. Dineen S. Complex Analysis on Infinite Dimensional Spaces. Springer-Verlag, London, 1999.
  9. Gámez-Merino J.L., Muñoz-Fernández G.A., Sánchez V.M., Seoane-Sepúlveda J.B. Inequalities for polynomials on the unit square via the Krein-Milman Theorem. J. Convex Anal. 2013, 20 (1), 125-142.
  10. Grecu B.C. Geometry of three-homogeneous polynomials on real Hilbert spaces. J. Math. Anal. Appl. 2000, 246 (1), 217-229. doi: 10.1006/jmaa.2000.6783
  11. Grecu B.C. Smooth 2-homogeneous polynomials on Hilbert spaces. Arch. Math. (Basel) 2001, 76 (6), 445-454. doi: 10.1007/PL00000456
  12. Grecu B.C. Geometry of 2-homogeneous polynomials on $l_p$ spaces, $ 1< p < ∞ $. J. Math. Anal. Appl. 2002, 273 (2), 262-282. doi: 10.1016/S0022-247X(02)00217-2
  13. Grecu B.C. Extreme 2-homogeneous polynomials on Hilbert spaces. Quaest. Math. 2002, 25 (4), 421-435. doi: 10.2989/16073600209486027
  14. Grecu B.C. Geometry of homogeneous polynomials on two-dimensional real Hilbert spaces. J. Math. Anal. Appl. 2004, 293 (2), 578-588. doi: 10.1016/j.jmaa.2004.01.020
  15. Grecu B.C., Muñoz-Fernández G.A., Seoane-Sepúlveda J.B. The unit ball of the complex $P(^3H)$. Math. Z. 2009, 263, 775-785. doi: 10.1007/s00209-008-0438-y
  16. Kim S.G. Exposed 2-homogeneous polynomials on $L_P^2$, $1\leq P\leq \infty$. Math. Proc. R. Ir. Acad. 2007, 107A (2), 123-129.
  17. Kim S.G. The unit ball of ${\mathcal L}_s(^2l_{\infty}^2)$. Extracta Math. 2009, 24 (1), 17-29.
  18. Kim S.G. The unit ball of ${\mathcal P}(^2d_{*}(1, w)^2)$. Math. Proc. R. Ir. Acad. 2011, 111A (2), 77-92.
  19. Kim S.G. The unit ball of ${\mathcal L}_s(^2d_*(1, w)^2)$. Kyungpook Math. J. 2013, 53, 295-306.
  20. Kim S.G. Smooth polynomials of ${\mathcal P}(^2d_*(1,w)^2)$. Math. Proc. R. Ir. Acad. 2013, 113A (1), 45-58.
  21. Kim S.G. Extreme bilinear forms of ${\mathcal L}(^2d_*(1,w)^2)$. Kyungpook Math. J. 2013, 53 (2), 625-638.
  22. Kim S.G. Exposed symmetric bilinear forms of ${\mathcal L}_s(^2d_*(1, w)^2)$. Kyungpook Math. J. 2014, 54 (3), 341-347.
  23. Kim S.G. Polarization and unconditional constants of ${\mathcal P}(^2d_{*}(1, w)^2)$. Commun. Korean Math. Soc. 2014, 29 (3), 421-428. doi: 10.4134/CKMS.2014.29.3.421
  24. Kim S.G. Exposed bilinear forms of ${\mathcal L}(^2d_*(1,w)^2)$. Kyungpook Math. J. 2015, 55 (1), 119-126.
  25. Kim S.G. Exposed 2-homogeneous polynomials on the two-dimensional real predual of Lorentz sequence space. Mediterr. J. Math. 2016, 13, 2827-2839. doi: 10.1007/s00009-015-0658-4
  26. Kim S.G. The unit ball of ${\mathcal L}(^2 {\mathbb R}^2_{h(w)})$. Bull. Korean Math. Soc. 2017, 54 (2), 417-428. doi: 10.4134/BKMS.b150851
  27. Kim S.G. Extremal problems for ${\mathcal L}_s(^2\mathbb{R}_{h(w)}^2)$. Kyungpook Math. J. 2017, 57 (2), 223-232.
  28. Kim S.G. The unit ball of ${\mathcal L}_s(^2l_{\infty}^3)$. Comment. Math. (Prace Mat.) 2017, 57 (1), 1-7. doi: 10.14708/cm.v57i1.1230
  29. Kim S.G. The geometry of ${\mathcal L}_s(^3l_{\infty}^2$). Commun. Korean Math. Soc. 2017, 32 (4), 991-997.\\ doi: 10.4134/CKMS.c170016
  30. Kim S.G. Extreme $2$-homogeneous polynomials on the plane with a hexagonal norm and applications to the polarization and unconditional constants. Studia Sci. Math. Hungar. 2017, 54 (3), 362-393. doi: 10.1556/012.2017.54.3.1371
  31. Kim S.G. The geometry of ${\mathcal L}(^3l_{\infty}^2)$ and optimal constants in the Bohnenblust-Hill inequality for multilinear forms and polynomials. Extracta Math. 2018, 33 (1), 51-66.
  32. Kim S.G. Extreme bilinear forms on $\mathbb{R}^n$ with the supremum norm. Period. Math. Hungar. 2018, 77, 274-290. doi: 10.1007/s10998-018-0246-z
  33. Kim S.G. Exposed polynomials of ${\mathcal P}(^2 \mathbb{R}^2_{h(\frac{1}{2})})$. Extracta Math. 2018, 33 (2), 127-143.
  34. Kim S.G. Extreme and exposed points of ${\mathcal L}(^n l^2_{\infty})$ and ${\mathcal L}_s(^n l^2_{\infty})$. Extracta Math. 2020, 35 (2), 127-135. doi: 10.17398/2605-5686.35.2.127
  35. Kim S.G. The unit balls of ${\mathcal L}(^nl_{\infty}^m)$ and ${\mathcal L}_s(^nl_{\infty}^m)$. Studia Sci. Math. Hungar. 2020, 57 (3), 267-283. doi: 10.1556/012.2020.57.3.1470
  36. Kim S.G. The unit ball of ${\mathcal L}_s(^2 \mathbb{R}^3_{{\mathcal L}_s(^2l_{\infty}^2)})$. Preprint.
  37. Kim S.G., Lee S.H. Exposed 2-homogeneous polynomials on Hilbert spaces. Proc. Amer. Math. Soc. 2003, 131 (2), 449-453.
  38. Konheim A.G., Rivlin T.J. Extreme points of the unit ball in a space of real polynomials. Amer. Math. Monthly 1966, 73 (5), 505-507. doi: 10.2307/2315472
  39. Milev L., Naidenov N. Strictly definite extreme points of the unit ball in a polynomial space. C. R. Acad. Bulgare Sci. 2008, 61 (11), 1393-1400.
  40. Milev L., Naidenov N. Indefinite extreme points of the unit ball in a polynomial space. Acta Sci. Math. (Szeged) 2011, 77 (3-4), 409-424.
  41. Milev L., Naidenov N. Semidefinite extreme points of the unit ball in a polynomial space. J. Math. Anal. Appl. 2013, 405 (2), 631-641. doi: 10.1016/j.jmaa.2013.04.026
  42. Muñoz-Fernández G.A., Pellegrino D., Seoane-Sepúlveda J.B., Weber A. Supremum norms for 2-homogeneous polynomials on circle sectors. J. Convex Anal. 2014, 21 (3), 745-764.
  43. Muñoz-Fernández G.A., Révész S.G.,Seoane-Sepúlveda J.B. Geometry of homogeneous polynomials on non symmetric convex bodies. Math. Scand. 2009, 105 (1), 147-160. doi: 10.7146/math.scand.a-15111
  44. Muñoz-Fernández G.A., Seoane-Sepúlveda J.B. Geometry of Banach spaces of trinomials. J. Math. Anal. Appl. 2008, 340 (2), 1069-1087. doi: 10.1016/j.jmaa.2007.09.010
  45. Neuwirth S. The maximum modulus of a trigonometric trinomial. J. Anal. Math. 2008, 104, 371-396. doi: 10.1007/s11854-008-0028-2
  46. Révész S.G. Minimization of maxima of nonnegative and positive definite cosine polynomials with prescribed first coefficients. Acta Sci. Math. (Szeged) 1995, 60 (3-4), 589-608.
  47. Ryan R.A., Turett B. Geometry of spaces of polynomials. J. Math. Anal. Appl. 1998, 221 (2), 698-711. doi: 10.1006/jmaa.1998.5942