We solve the operator equations where the unknown is the linear operator , and obtain the solutions in three equivalent forms: as infinite-order differential operators with variable coefficients, as "translation" operators and as integral operators.
The main topic of this paper is the interaction between vortex density waves and high-frequency second sound in counterflow superfluid turbulence. To this end a thermodynamical model including vortex flux as independent variable is considered. This choice is crucial for the study of the transition of the behavior of the vortex-density perturbations from diffusive to propagative, which is necessary to interpret the details of the high-frequency second sound waves.
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