A Riesz basis for Bargmann-Fock space related to sampling and interpolation
نویسندگان
چکیده
منابع مشابه
Sampling and Interpolation in Bargmann-fock Spaces of Polyanalytic Functions
We give a complete characterization of all lattice sampling and interpolating sequences in the Fock space of polyanalytic functions (polyFock spaces), displaying a ”Nyquist rate” which increases with the degree of polyanaliticity. This is done introducing a unitary mapping between vector valued Hilbert spaces and poly-Fock spaces. This mapping extends Bargmann ́s theory to polyanalytic spaces. T...
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ABSTRACT. We study those smooth complex hypersurfaces W in C having the property that all holomorphic functions of finite weighted L norm on W extend to entire functions with finite weighted L norm. Such hypersurfaces are called interpolation hypersurfaces. We also examine the dual problem of finding all sampling hypersurfaces, i.e., smooth hypersurfaces W in C such that any entire function wit...
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Usually in quantum mechanics the Heisenberg algebra is generated by operators of position and momentum. The algebra is then represented on an Hilbert space of square integrable functions. Alternatively one generates the Heisenberg algebra by the raising and lowering operators. It is then natural to represent it on the Bargmann Fock space of holomorphic functions. In the following I show that th...
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ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 1992
ISSN: 0004-2080
DOI: 10.1007/bf02384875