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Exponential bounds for noncommuting systems of matrices

100%
Jefferies B.
Studia Mathematica
|
2001
|
tom 144
|
nr 3
197-207
EN
It is shown that a finite system T of matrices whose real linear combinations have real spectrum satisfies a bound of the form $||e^{i⟨T,ζ⟩}|| ≤ C(1+|ζ|)^{s}e^{r|ℑ ζ|}$. The proof appeals to the monogenic functional calculus.
2
Content available remote

Function theory in sectors

100%
Jefferies B.
Studia Mathematica
|
2004
|
tom 163
|
nr 3
257-287
EN
It is shown that there is a one-to-one correspondence between uniformly bounded holomorphic functions of n complex variables in sectors of ℂⁿ, and uniformly bounded functions of n+1 real variables in sectors of $ℝ^{n+1}$ that are monogenic functions in the sense of Clifford analysis. The result is applied to the construction of functional calculi for n commuting operators, including the example of differentiation operators on a Lipschitz surface in $ℝ^{n+1}$.
3
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The monogenic functional calculus

51%
Jefferies B., McIntosh A., Picton-Warlow J.
Studia Mathematica
|
1999
|
tom 136
|
nr 2
99-119
EN
A study is made of a symmetric functional calculus for a system of bounded linear operators acting on a Banach space. Finite real linear combinations of the operators have real spectra, but the operators do not necessarily commute with each other. Analytic functions of the operators are formed by using functions taking their values in a Clifford algebra.
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