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Article

Approximating Functions of Positive Compact Operators by Using Bell Polynomials

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Department of Research and Development, The Antenna Company, High Tech Campus 29, 5656 AE Eindhoven, The Netherlands
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Department of Electrical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
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Department of Mathematics and Physics, Roma Tre University, Largo San Leonardo Murialdo 1, 00146 Rome, Italy
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Department of Mathematics, International Telematic University UniNettuno, Corso Vittorio Emanuele II 39, 00186 Rome, Italy
*
Author to whom correspondence should be addressed.
Axioms 2020, 9(3), 73; https://doi.org/10.3390/axioms9030073
Received: 10 June 2020 / Revised: 23 June 2020 / Accepted: 24 June 2020 / Published: 30 June 2020
(This article belongs to the Special Issue Special Functions and Their Applications)
After recalling the most important properties of the Bell polynomials, we show how to approximate a positive compact operator by a suitable matrix. Then, we derive a representation formula for functions of the obtained matrix, which can be considered as an approximate value for the functions of the corresponding operator. View Full-Text
Keywords: resolvent; Bell polynomials; orthogonal invariants; Robert’s formulas; positive compact operators; matrix functions resolvent; Bell polynomials; orthogonal invariants; Robert’s formulas; positive compact operators; matrix functions
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MDPI and ACS Style

Caratelli, D.; Natalini, P.; Ricci, P.E. Approximating Functions of Positive Compact Operators by Using Bell Polynomials. Axioms 2020, 9, 73. https://doi.org/10.3390/axioms9030073

AMA Style

Caratelli D, Natalini P, Ricci PE. Approximating Functions of Positive Compact Operators by Using Bell Polynomials. Axioms. 2020; 9(3):73. https://doi.org/10.3390/axioms9030073

Chicago/Turabian Style

Caratelli, Diego, Pierpaolo Natalini, and Paolo Emilio Ricci. 2020. "Approximating Functions of Positive Compact Operators by Using Bell Polynomials" Axioms 9, no. 3: 73. https://doi.org/10.3390/axioms9030073

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