The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Effective computation of the first Lyapunov quantities for a planar differential equation”

Preparation theorems for matrix valued functions

Nils Dencker (1993)

Annales de l'institut Fourier

Similarity:

We generalize the Malgrange preparation theorem to matrix valued functions F ( t , x ) ∈ C ∞ ( R × R n ) satisfying the condition that t ↦ det F ( t , 0 ) vanishes to finite order at t = 0 . Then we can factor F ( t , x ) = C ( t , x ) P ( t , x ) near (0,0), where C ( t , x ) ∈ C ∞ is inversible and P ( t , x ) is polynomial function of t depending C ∞ on x . The preparation is (essentially) unique, up to functions vanishing to infinite order at x = 0 , if we impose some additional conditions on P ( t , x ) . We also have a generalization of the division theorem, and analytic versions generalizing the Weierstrass...

A necessary condition of local solvability for pseudo-differential equations with double characteristics

Fernando Cardoso, François Trèves (1974)

Annales de l'institut Fourier

Similarity:

Pseudodifferential operators P ( x , D ) ∼ ∑ j = 0 + ∞ P m - j ( x , D ) are studied, from the viewpoint of local solvability and under the assumption that, micro-locally, the principal symbol factorizes as P m = Q L 2 with Q elliptic, homogeneous of degree m - 2 , and L homogeneous of degree one, satisfying the following condition : there is a point ( x 0 , ξ 0 ) in the characteristic variety L = 0 and a complex number z such that d ξ Re ( z L ) ≠ 0 at ( x 0 , ξ 0 ) and such that the restriction of Im ( z L ) to the bicharacteristic strip of Re ( z L ) vanishes of order k < + ∞ at ( x 0 , ξ 0 ) , changing sign there from...

On the closure of spaces of sums of ridge functions and the range of the X -ray transform

Jan Boman (1984)

Annales de l'institut Fourier

Similarity:

For a ∈ R n ∖ { 0 } and Ω an open bounded subset of R n definie L p ( Ω , a ) as the closed subset of L p ( Ω ) consisting of all functions that are constant almost everywhere on almost all lines parallel to a . For a given set of directions a ν ∈ R n ∖ { 0 } , ν = 1 , ... , m , we study for which Ω it is true that the vector space ( * ) L p ( Ω , a 1 ) + ⋯ + L p ( Ω , a m ) is a closed subspace of L p ( Ω ) . This problem arizes naturally in the study of image reconstruction from projections (tomography). An essentially equivalent problem is to decide whether a certain matrix-valued differential operator...