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Showing 1 to 4 of 4 for “"Generalized Fourier Series"”.
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Notes on generalized Fourier series with application to gravitational field determination
… square integrable functions L². Let f𝜖L². The generalized Fourier series of f with respect to {(}φ<sub>n</sub>(x)} is the series ∑<sub>n=0</sub><sup>∞</sup> (f, φ<sub>n</sub>) φ<sub>n</sub>(x), where (f, φ<sub>n</sub>) is the inner product of the functions f an φ<sub>n</sub>. The e existence of …
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A Development of Orthogonal Functions as Series Solutions of the Partial Differential Equations of Physics
… problem in Physics leads to the solution in generalized Fourier Series. The conditions to be met in problems of this sort are generally the Partial Differential Equation and several unique physical conditions which are imposed on the distribution sought after. The problem is solved when a …
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Characterizing Neurotransmitter Receptor Activation with a Perturbation Based Decomposition Method
… for this application, and compared to a generalized Fourier series approach. The resultant estimator is valid for decomposition of multiple-receptor compound postsynaptic potentials as well as single-receptor compound postsynaptic potentials. The estimator also yields a satisfactory …
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Discrete Sparse Fourier Hermite Approximations in High Dimensions
<p>In this dissertation, the discrete sparse Fourier Hermite approximation of a function in a specified Hilbert space of arbitrary dimension is defined, and theoretical error bounds of the numerically computed approximation are proven. Computing the Fourier Hermite approximation in high dimensions …