Relevant bibliographies by topics / Entrywise Positivity Preservers

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Entrywise Positivity Preservers'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Entrywise Positivity Preservers"

1

Khare, Apoorva, and Terence Tao. "On the sign patterns of entrywise positivity preservers in fixed dimension." American Journal of Mathematics 143, no. 6 (2021): 1863–929. http://dx.doi.org/10.1353/ajm.2021.0049.

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Khare, Apoorva. "Smooth entrywise positivity preservers, a Horn–Loewner master theorem, and symmetric function identities." Transactions of the American Mathematical Society 375, no. 3 (2021): 2217–36. http://dx.doi.org/10.1090/tran/8563.

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A special case of a fundamental result of Loewner and Horn [Trans. Amer. Math. Soc. 136 (1969), pp. 269–286] says that given an integer n ⩾ 1 n \geqslant 1 , if the entrywise application of a smooth function f : ( 0 , ∞ ) → R f : (0,\infty ) \to \mathbb {R} preserves the set of n × n n \times n positive semidefinite matrices with positive entries, then f f and its first n − 1 n-1 derivatives are non-negative on ( 0 , ∞ ) (0,\infty ) . In a recent joint work with Belton–Guillot–Putinar [J. Eur. Math. Soc., in press], we proved a stronger version, and used it to strengthen the Schoenberg–Rudin c
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Belton, Alexander, Dominique Guillot, Apoorva Khare, and Mihai Putinar. "Schur polynomials and matrix positivity preservers." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings, 28th... (April 22, 2020). http://dx.doi.org/10.46298/dmtcs.6408.

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International audience A classical result by Schoenberg (1942) identifies all real-valued functions that preserve positive semidefi- niteness (psd) when applied entrywise to matrices of arbitrary dimension. Schoenberg's work has continued to attract significant interest, including renewed recent attention due to applications in high-dimensional statistics. However, despite a great deal of effort in the area, an effective characterization of entrywise functions preserving positivity in a fixed dimension remains elusive to date. As a first step, we characterize new classes of polynomials preserv
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Dissertations / Theses on the topic "Entrywise Positivity Preservers"

1

Vishwakarma, Prateek Kumar. "Positivity preservers forbidden to operate on diagonal blocks." Thesis, 2021. https://etd.iisc.ac.in/handle/2005/5537.

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The question of which functions acting entrywise preserve positive semidefiniteness has a long history, beginning with the Schur product theorem [Crelle 1911], which implies that absolutely monotonic functions (i.e., power series with nonnegative coefficients) preserve positivity on matrices of all dimensions. A famous result of Schoenberg and of Rudin [Duke Math. J. 1942, 1959] shows the converse: there are no other such functions. Motivated by modern applications, Guillot and Rajaratnam [Trans. Amer. Math. Soc. 2015] classified the entrywise positivity preservers in all dimensions,
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Books on the topic "Entrywise Positivity Preservers"

1

Khare, Apoorva. Matrix Analysis and Entrywise Positivity Preservers. Cambridge University Press, 2021.

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Khare, Apoorva. Matrix Analysis and Entrywise Positivity Preservers. Cambridge University Press, 2022.

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Book chapters on the topic "Entrywise Positivity Preservers"

1

"Entrywise Powers Preserving Positivity, Monotonicity, and Superadditivity." In Matrix Analysis and Entrywise Positivity Preservers. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781108867122.011.

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"Preservers of Loewner Positivity on Kernels." In Matrix Analysis and Entrywise Positivity Preservers. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781108867122.022.

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"Entrywise Polynomial Preservers and Horn–Loewner-Type Conditions." In Matrix Analysis and Entrywise Positivity Preservers. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781108867122.029.

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"Entrywise Powers Preserving Positivity in a Fixed Dimension." In Matrix Analysis and Entrywise Positivity Preservers. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781108867122.008.

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"Entrywise Preservers of Positivity on Matrices with Zero Patterns." In Matrix Analysis and Entrywise Positivity Preservers. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781108867122.010.

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"Midconvex Implies Continuity, and 2 × 2 Preservers." In Matrix Analysis and Entrywise Positivity Preservers. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781108867122.009.

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"The Schur Product Theorem and Nonzero Lower Bounds." In Matrix Analysis and Entrywise Positivity Preservers. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781108867122.005.

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"Stronger Vasudeva and Schoenberg Theorems via Bernstein’s Theorem." In Matrix Analysis and Entrywise Positivity Preservers. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781108867122.018.

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9

"Exercises." In Matrix Analysis and Entrywise Positivity Preservers. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781108867122.035.

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"Exercises." In Matrix Analysis and Entrywise Positivity Preservers. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781108867122.013.

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