Claude Mitschi, Michael F. Singer
The usual Galois theory of polynomial equations allows one to associate a group to a polynomial in such a way that the algebraic properties of the roots of the polynomial are reflected in properties...
On the generalized Riemann-Hilbert problem with irregular singularities (2007)
Bolibruch, A. A., Malek, Stéphane, Mitschi, Claude
We give sufficient conditions, on data including the monodromy representation, the Stokes matrices and the Poincare ranks at prescribed singularities, to solve the generalized Riemann-Hilbert problem...
On the constructive inverse problem in differential Galois theory (2005)
William J. Cook, Claude Mitschi, Michael F. Singer
We give sufficient conditions for a differential equation to have a given semisimple group as its Galois group. For any group G with G 0 = G1 ·... · Gr where each Gi is a simple group of type Aℓ,...
On the constructive inverse problem in differential Galois theory (2005)
William J. Cook, Claude Mitschi, Michael F. Singer
We give sufficient conditions for a differential equation to have a given semisimple group as its Galois group. For any group G with G 0 = G 1 · ·· · ·G r, where each G i is a simple group of...
On the Constructive Inverse Problem in Differential Galois Theory (2004)
Cook, William J., Mitschi, Claude, Singer, Michael F.
We give sufficient conditions for a linear differential equation to have a given semisimple group as its Galois group. For any linear algebraic group G given as a semidirect product of a finite...
On the generalized Riemann-Hilbert problem with irregular singularities (2004)
Bolibruch, Andrey, Malek, Stéphane, Mitschi, Claude
We give sufficient conditions, on data including the monodromy representation, the Stokes matrices and the Poincaré rank at prescribed singularities, to solve the generalized Riemann-Hilbert problem...
On the generalized Riemann-Hilbert problem with irregular singularities (2004)
Bolibruch, Andrey, Malek, Stéphane, Mitschi, Claude
We give sufficient conditions, on data including the monodromy representation, the Stokes matrices and the Poincaré rank at prescribed singularities, to solve the generalized Riemann-Hilbert problem...
Solvable-by-finite groups as differential Galois groups (2002)
Mitschi, Claude, Singer, Michael F.
We prove the inverse problem of differential Galois theory over the differential field k=C(x), where C is an algebraic closed field of characteristic zero, for linear algebraic groups G over CC with...
Solvable-by-finite groups as differential Galois groups (2002)
Mitschi, Claude, Singer, Michael F.
We prove the inverse problem of differential Galois theory over the differential field k=C(x), where C is an algebraic closed field of characteristic zero, for linear algebraic groups G over CC with...
On Magid's approach to the inverse problem in differential Galois theory. (1996)
Kovacic, Jerry, Mitschi, Claude, Singer, Michael F.
We present counterexamples to Theorem 7.3 and Theorem 7.13 in {em Lectures in Differential Galois Theory} by A. Magid, University Lecture Series, Vol. 7, AMS 1994.
On Magid's approach to the inverse problem in differential Galois theory. (1996)
Kovacic, Jerry, Mitschi, Claude, Singer, Michael F.
We present counterexamples to Theorem 7.3 and Theorem 7.13 in {em Lectures in Differential Galois Theory} by A. Magid, University Lecture Series, Vol. 7, AMS 1994.
Connected Linear Groups as Differential Galois Groups over $C(x)$. (1995)
Mitschi, Claude, Singer, Michael F.
We generalize results of Kovacic to solve the inverse problem in differential Galois theory for connected linear groups, over $C(x)$ where $C$ is an arbitrary algebraically closed field $C$ of...
Connected Linear Groups as Differential Galois Groups over $C(x)$. (1995)
Mitschi, Claude, Singer, Michael F.
We generalize results of Kovacic to solve the inverse problem in differential Galois theory for connected linear groups, over $C(x)$ where $C$ is an arbitrary algebraically closed field $C$ of...
On Ramis's solution of the local inverse problem of differential Galois theory. (1994)
Mitschi, Claude, Singer, Michael F.
Recently, J.P. Ramis gave necessary and sufficient conditions for a linear algebraic group to be the Galois group of a Picard-Vessiot extension of the field ${\bf C}\{x\}[x^{-1}]$ of germs of...
On Ramis's solution of the local inverse problem of differential Galois theory. (1994)
Mitschi, Claude, Singer, Michael F.
Recently, J.P. Ramis gave necessary and sufficient conditions for a linear algebraic group to be the Galois group of a Picard-Vessiot extension of the field ${\bf C}\{x\}[x^{-1}]$ of germs of...