Frames for Fréchet spaces XF with respect to Fréchet sequence spaces ΘF are studied and conditions, implying series expansions in XF and X ∗ F , are determined. If {gi}i=1 is a Θ0-frame for X0, we construct a sequence {Xs}s∈N0 , Xs ⊂ Xs−1, s ∈ N, for given ΘF , respectively a sequence {Θs}s∈N0 , Θs ⊂ Θs−1, s∈N, for given XF , so that {gi}i=1 is a pre-F -frame (or F -frame) for XF with respect t...

There has been fascinating work on creating artistic transformations of images by Gatys et al. This was revolutionary in how we can in some sense alter the “style” of an image while generally preserving its “content”. In this work, we present a method for creating new sounds using a similar approach. For demonstration, we investigate two different tasks, resulting in bandwidth expansion/compres...

We firstly consider an investor faced with the classical Merton problem of optimal investment in a log-Brownian asset and a fixed-interest bond, but constrained only to change portfolio (and, if relevant, consumption) choices at times which are a multiple of h . We show that the cost of this constraint can be well described by a power series expansion in h , the first few terms of which we dete...

Starting from the power series expansions of (sin −1 x) q , for 1 ≤ q ≤ 4, formulae are obtained for the sum of several infinite series. Some of these evaluations involve ζ(3).

We define p-adic multiple zeta and log gamma functions using multiple Volkenborn integrals, and develop some of their properties. Although our functions are close analogues of classical Barnes multiple zeta and log gamma functions and have many properties similar to them, we find that our p-adic analogues also satisfy reflection functional equations which have no analogues to the complex case. ...

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