Tannaka's theorem states that a linear algebraic group G is determined by the category of finite-dimensional G-modules and the forgetful functor. We extend this result to linear differential algebraic groups by introducing a category corresponding to their representations and show how this category determines such a group.
We provide conditions for a category with a fiber functor to be equivalent to the category of representations of a linear differential algebraic group. This generalizes the notion of a neutral Tannakian category used to characterize the category of representations of a linear algebraic group , .
The automatic real-time detection of spike-wave discharges (SWDs), the electroencephalographic hallmark of absence seizures, would provide a complementary tool for rapid interference with electrical deep brain stimulation in both patients and animal models. This paper describes a real-time detection algorithm for SWDs based on continuous wavelet analyses in… (More)
We propose an algorithm for transforming a characteristic decomposition of a radical differential ideal from one ranking into another. The algorithm is based on a new bound: we show that, in the ordinary case, for any ranking, the order of each element of the canonical characteristic set of a characterizable differential ideal is bounded by the order of the… (More)
We give the first known bound for orders of differentiations in differential Nullstel-lensatz for both partial and ordinary algebraic differential equations. This problem was previously addressed in  but no complete solution was given. Our result is a complement to the corresponding result in algebraic geometry, which gives a bound on degrees of… (More)
We deal with aspects of the direct and inverse problems in the parameterized Picard-Vessiot (PPV) theory. It is known that, for certain fields, a linear differential algebraic group (LDAG) G is a PPV Galois group over these fields if and only if G contains a Kolchin-dense finitely generated group. We show that for a class of LDAGs G, including unipotent… (More)
We develop the representation theory for reductive linear differential algebraic groups (LDAGs). In particular, we exhibit an explicit sharp upper bound for orders of derivatives in differential representations of reductive LDAGs, extending existing results, which were obtained for SL 2 in the case of just one derivation. As an application of the above… (More)
Linear differential algebraic groups (LDAGs) measure differential algebraic dependencies among solutions of linear differential and difference equations with parameters, for which LDAGs are Galois groups. The differential representation theory is a key to developing algorithms computing these groups. In the rational representation theory of algebraic… (More)
We define a differential Tannakian category and show that under a natural assumption it has a fiber functor. If in addition this category is neutral, that is, the target category for the fiber functor are finite dimensional vector spaces over the base field, then it is equivalent to the category of representations of a (pro-)linear differential algebraic… (More)
We consider the Rosenfeld-Gröbner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials F , let M (F) be the sum of maximal orders of differential indeterminates occurring in F. We propose a modification of… (More)