Abstract. Bilinear pseudodifferential operators with symbols in the bilinear analog of all the Hörmander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise results about which classes are closed under transposition and can be characterized in terms of asymptotic expansions are presented. This work extends the results for more limited classes studied before in the literature and, hence, allows the use of the symbolic calculus (when it exists) as an alternative way to recover the boundedness on products of Lebesgue spaces for the classes that yield operators with bilinear Calderón-Zygmund kernels. Some boundedness properties for other classes with estimates in the form of Leibniz' rule are presented as well.
Abstract. Bilinear pseudodifferential operators with symbols in the bilinear analog of all the Hörmander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise results about which classes are closed under transposition and can be characterized in terms of asymptotic expansions are presented. This work extends the results for more limited classes studied before in the literature and, hence, allows the use of the symbolic calculus (when it exists) as an alternative way to recover the boundedness on products of Lebesgue spaces for the classes that yield operators with bilinear Calderón-Zygmund kernels. Some boundedness properties for other classes with estimates in the form of Leibniz' rule are presented as well.
We establish boundedness properties on products of weighted Lebesgue, Hardy, and amalgam spaces of certain paraproducts and bilinear pseudodifferential operators with mild regularity. We do so by showing that these operators can be realized as generalized bilinear Calderón-Zygmund operators.
Accurate lineshape functions for modeling fluorescence line narrowing (FLN) difference spectra (DeltaFLN spectra) in the low-fluence limit are derived and examined in terms of the physical interpretation of various contributions, including photoproduct absorption and emission. While in agreement with the earlier results of Jaaniso [Proc. Est. Acad. Sci., Phys., Math. 34, 277 (1985)] and Funfschilling et al. [J. Lumin. 36, 85 (1986)], the derived formulas differ substantially from functions used recently [e.g., M. Ratsep et al., Chem. Phys. Lett. 479, 140 (2009)] to model DeltaFLN spectra. In contrast to traditional FLN spectra, it is demonstrated that for most physically reasonable parameters, the DeltaFLN spectrum reduces simply to the single-site fluorescence lineshape function. These results imply that direct measurement of a bulk-averaged single-site fluorescence lineshape function can be accomplished with no complicated extraction process or knowledge of any additional parameters such as site distribution function shape and width. We argue that previous analysis of DeltaFLN spectra obtained for many photosynthetic complexes led to strong artificial lowering of apparent electron-phonon coupling strength, especially on the high-energy side of the pigment site distribution function.
We present exact equations for the low-fluence non-line-narrowed (NLN) nonphotochemical hole-burning (NPHB) spectrum of an excitonically coupled dimer (for arbitrary coupling strength) under the assumption that postburn and preburn site energies are independent. The equations provide a transparent view into the contributions of various effects to the NPHB spectrum. It is demonstrated that the NPHB spectrum in dimers is largely dominated by the statistical reshuffling of site energies and by altered excitonic transition energies of both excitonic states (in contrast with only the lowest state). For comparison of these results with those from larger excitonically coupled systems, the low-fluence NLN NPHB spectrum obtained for the CP47 complex (a 16-pigment core antenna complex of Photosystem II) is also calculated using Monte Carlo simulations. In this larger system it is shown that the NPHB spectra for individual excitonic states are not entirely conservative (although the changes in average oscillator strength for the higher excitonic states are in most cases less than 1%), a feature which we argue is due primarily to reordering of the contributions of various pigments to the excitonic states. We anticipate that a better understanding of NPHB spectra obtained for various photosynthetic complexes and their simultaneous fits with other optical spectra (e.g., absorption, emission, and circular dichroism spectra) will provide more insight into the underlying electronic structures of various photosynthetic systems.
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