# A unifying perspective on linear continuum equations prevalent in science. Part VI: rapidly converging series expansions for their solution

@article{Milton2020AUP, title={A unifying perspective on linear continuum equations prevalent in science. Part VI: rapidly converging series expansions for their solution}, author={Graeme W. Milton}, journal={arXiv: Mathematical Physics}, year={2020} }

We obtain rapidly convergent series expansions of resolvents of operators taking the form ${\bf A}=\Gamma_1{\bf B}\Gamma_1$ where $\Gamma_1({\bf k})$ is a projection that acts locally in Fourier space and ${\bf B}({\bf x})$ is an operator that acts locally in real space. Such resolvents arise naturally when one wants to solve any of the large class of linear physical equations surveyed in Parts I, II, III, and IV that can be reformulated as problems in the extended abstract theory of composites…

## 3 Citations

A unifying perspective on linear continuum equations prevalent in physics. Part VII: Boundary value and scattering problems

- Physics, Mathematics
- 2021

We consider simply connected bodies or regions of finite extent in space or space-time and write conservation laws associated with the equations in Parts I-IV. We review earlier work where, for…

A unifying perspective on linear continuum equations prevalent in physics. Part II: Canonical forms for time-harmonic equations

- Physics, Mathematics
- 2020

Following some past advances, we reformulate a large class of linear continuum science equations in the format of the extended abstract theory of composites so that we can apply this theory to better…

A unifying perspective on linear continuum equations prevalent in science. Part I: Canonical forms for static, steady, and quasistatic equations

- Physics, Mathematics
- 2020

Following some past advances, we reformulate a large class of linear continuum science equations in the format of the extended abstract theory of composites so that we can apply this theory to better…

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