103
Views
1
CrossRef citations to date
0
Altmetric
Research Article

On an integral representation of the normalized trace of the k-th symmetric tensor power of matrices and some applications

ORCID Icon, & ORCID Icon
Pages 1198-1216 | Received 08 Jun 2021, Accepted 15 Feb 2022, Published online: 05 Apr 2022

References

  • Bhatia R, Holbrook JAR. Unitary invariance and spectral variation. Linear Algebra Appl. 1987;95:43–68.
  • Kania T. A short proof of the fact that the matrix trace is the expectation of the numerical values. Am Math Mon. 2015;122(8):782–783.
  • Krantz SG. Function theory of several complex variables. Amer Math Soc; 2001. (AMS Chelsea Publishing Series).
  • Saitoh S. Theory of reproducing kernels and its applications. Harlow (UK): Longman Scientific and Technical; 1988.
  • Hunter DB. The positive-definiteness of the complete symmetric functions of even order. Proc Camb Philos Soc. 1977;82(2):255–258.
  • Rovena I, Temereanca LE. A note on the positivity of the even degree complete homogeneous symmetric polynomials. Mediterr J Math. 2019;16(1):1–16.
  • Cuttler A, Greene C, Skandera M. Inequalities for symmetric means. Eur J Comb. 2011;32(6):745–761.
  • Tong YL. An ordering theorem for conditionally independent and identically distributed random variables. Ann Statist. 1977;5:274–277.
  • Sra S. On inequalities for normalized Schur functions. Eur J Comb. 2016;51:492–494.
  • Harver DA. Matrix Algebra from a statistician's perspective. Berlin: Springer; 2008.
  • Henderson HV, Searle SR. The vec-permutation, the vec-operator and Kronecker products: a review. Linear Multilinear Algebra. 1981;9:271–288.
  • Axler S, Bourdon P, Wade R. Harmonic function theory. New York (NY): Springer; 2013. (Graduate texts in Mathematics; 137).
  • Folland GB. Real analysis. New York (NY): John Wiley; 1999.
  • Bauer W, Issa H. Commuting Toeplitz operators with quasi-homogeneous symbols on the Segal-Bargmann space. J Math Anal Appl. 2012;386:213–235.
  • Issa H. Construction of some classes of commutative Banach and C⋆-algebras of Toeplitz operators. C R Acad Sci Paris. 2019;357(1):389–394.
  • Issa H. The analysis of Toeplitz operators, commutative Toeplitz algebras and applications to heat kernel constructions. Göttingen: S.U.B; 2012.
  • Folland GB. How to integrate a polynomial over a sphere. AMS. 2001;108(5):446–448.
  • Rudin W. Function theory in the unit ball of Cn. Berlin: Springer; 2008.
  • Agbor D, Bauer W. Heat flow and an algebra of Toeplitz operators. Integral Equations Oper Theory. 2015;70:271–299.
  • Bauer W. Berezin-Toeplitz quantization and composition formulas. J Func Anal. 2009;256:3107–3142.
  • Coburn LA. On the Berezin-Toeplitz calculus. Proc Am Math Soc. 2007;129(11):3331–3338.
  • Macdonald I. Symmetric functions and Hall polynomials. 2nd ed. Oxford: Oxford mathematical monographs; 1995.
  • MacMahon PA. Combinatory analysis. Vol. I and II, Cambridge: Cambridge University Press; 1915–16.
  • Good IJ. A short proof of MacMahon's master theorem. Proc Camb Philos Soc. 1962;58:160.
  • Stein EM, Shakarchi R. Real analysis: measure theory, integration, and Hilbert spaces. Princeton (NJ): Princeton University Press; 2005. (Princeton Lectures in Analysis; 3).
  • Marshall AW, Olkin I, Arnold BC. Inequalities: theory of majorization and its applications. 2nd ed. New York (NY): Springer; 2011.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.