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A new functional calculus for noncommuting operators [PDF]
Journal of Functional Analysis, 2008 . In this paper we use the notion of slice monogenic functions introduced in a paper by Colombo, Sabadini and Struppa (see Israel J. Math. 2009) to define a new functional calculus for an n-tuple T=(T_1,..., T_n) of not necessarily commuting operators ...
Daniele Struppa +2 more
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Journal of the London Mathematical Society, 1995
The formula of Helffer and Sjöstrand for functions \(f(H)\) of a selfadjoint operator \(H\) is generalized and put into the real perspective. The author constructs a functional calculus for Banach space operators with real spectra and slowly increasing resolvents when approaching the spectrum.
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The formula of Helffer and Sjöstrand for functions \(f(H)\) of a selfadjoint operator \(H\) is generalized and put into the real perspective. The author constructs a functional calculus for Banach space operators with real spectra and slowly increasing resolvents when approaching the spectrum.
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Quantitative Finance, 2009
We extend some results of the Ito calculus to functionals of the current path of a process to reflect the fact that often the impact of randomness is cumulative and depends on the history of the pr...
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We extend some results of the Ito calculus to functionals of the current path of a process to reflect the fact that often the impact of randomness is cumulative and depends on the history of the pr...
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A functional presentation of Pi calculus
Science in China Series F Information Sciences, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the fractional calculus functions of a fractal function
Applied Mathematics-A Journal of Chinese Universities, 2002The authors introduce a new type of functions by the combination of fractional calculus with fractal functions and they discuss then some properties, in particular, the dimension of this function.
Yao, Kui, Su, Weiyi, Zhou, Songping
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Contraction of an Adapted Functional Calculus
Journal of Lie Theory, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cotton, P., Dooley, A. H.
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Properties of the Local Functional Calculus
Mathematical Proceedings of the Royal Irish Academy, 2002The main purpose of the present article is to develop the local functional calculus and to give some applications to local spectral theory. In order to express the results, assume that \(T\in B(X)\) has the single-valued extension property (SVEP) and let \(f\) be a holomorphic function on a neighborhood of a fixed compact subset \(K\) of \(\mathbb{C}\).
Bermúdez, Teresa +2 more
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Automated Function Analysis for Calculus
Mathematics in Computer Science, 2018When teaching function analysis, as part of college calculus, many of the same calculations repeat themselves, over and over again. These calculations are for proving limits (their existance and values, or perhaps the lack thereof), finding minima and maxima, determining continuity and differentiability at specific points, or for ranges, etc.
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Functional calculus for the Laguerre operator
Mathematische Zeitschrift, 2004In this paper, the author studies the \(L^p\) boundedness of spectral multipliers associated to the multidimensional Laguerre operator \({\mathcal L}_\alpha\) on the Euclidean space. It is known that the analysis of the Laguerre operator can be interpreted as the analysis of the Ornstein-Uhlenbeck operator acting on polyradial functions.
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Naturality of the Functional Calculus
Bulletin of the London Mathematical Society, 1982Schanuel, Stephen H., Zame, William R.
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