Abstract
We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener–Lévy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener–Hopf operators.
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Alpay D., Colombo F., Lewkowicz I., Sabadini I.: Realizations of slice hyperholomorphic generalized contractive and positive functions. Milan J. Math. 83(1), 91–144 (2015)
Bart H., Gohberg I., Kaashoek M.A.: Convolution equations and linear systems. Integral Equations Oper. Theory 5(3), 283–340 (1982)
Bochner S., Phillips R.S.: Absolutely convergent Fourier expansions for non-commutative normed rings. Ann. Math. 43(2), 409–418 (1942)
Brown, A., Halmos, P.R.: Algebraic properties of Toeplitz operators. J. Reine. Angew. Math. 213, 89–102 (1963/1964)
Colombo, F., Sabadini, I., Struppa, D.C.: Noncommutative functional calculus, progress in mathematics, vol. 289. Birkhäuser/Springer, Basel AG, Basel (2011) (Theory and applications of slice hyperholomorphic functions)
Devinatz, A.: On Wiener-Hopf operators, functional analysis (Proc. Conf., Irvine, Calif., 1966), pp. 81–118. Academic Press, London; Thompson Book Co., Washington, D.C. (1967)
Fliess M.: Matrices de Hankel. J. Math. Pures Appl. 53(9), 197–222 (1974)
Gentili, G., Stoppato, C., Struppa, D.C.: Regular functions of a quaternionic variable. Springer Monographs in Mathematics, Springer, Heidelberg (2013)
Gohberg, I., Goldberg, S., Kaashoek, M.A.: Classes of linear operators. vol. II, operator theory: advances and applications, vol. 63. Birkhäuser Verlag, Basel (1993)
Lam, T.Y.: A first course in noncommutative rings, Graduate Texts in Mathematics, 2nd edn., vol. 131. Springer, New York (2001)
Rudin, W.: Real and complex analysis, 3rd edn. McGraw-Hill Book Co., New York (1987)
Wiener N.: Generalized harmonic analysis and Tauberian theorems. The M.I.T. Press, Cambridge, Mass.-London (1966)
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D. Alpay thanks the Earl Katz family for endowing the chair which supported his research. D. P. Kimsey gratefully acknowledges the support of a Kreitman postdoctoral fellowship. F. Colombo and I. Sabadini acknowledge the Center for Advanced Studies of the Mathematical Department of the Ben-Gurion University of the Negev for the support and the kind hospitality during the period in which part of this paper has been written.
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Alpay, D., Colombo, F., Kimsey, D.P. et al. Wiener Algebra for the Quaternions. Mediterr. J. Math. 13, 2463–2482 (2016). https://doi.org/10.1007/s00009-015-0634-z
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DOI: https://doi.org/10.1007/s00009-015-0634-z