A new formulation for collisional kinetic theory is presented based on the use of Lietransform methods to eliminate fast orbital time scales from a general bilinear collision operator. As an application of this new formalism, a general guiding-center bilinear FokkerPlanck (FP) collision operator is derived following the elimination of the fast gyromotion time scale of a charged particle moving ...

We utilize the Bellman function technique to prove a bilinear dimension-free inequality for the Hermite operator. The Bellman technique is applied here to a non-local operator, which at first did not seem to be possible. An indispensable tool in order to make the proofs dimension-free is a certain linear algebra lemma concerning three bilinear forms. As a consequence of our bilinear inequality ...

The aim of this paper is to study differential properties of orthogonal polynomials with respect to a discrete Laguerre–Sobolev bilinear form with mass point at zero. In particular we construct the orthogonal polynomials using certain Casorati determinants. Using this construction, we prove that they are eigenfunctions of a differential operator (which will be explicitly constructed). Moreover,...

We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most r. We apply these methods to several cases including the case r = 6 in the space of bilinear maps C × C → C. This space of bilinear maps includes the matrix multiplication operator M2 for two by two matrices. We show these newly obtained polynomials do not vanish on the matrix ...

We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most r. We apply these methods to several cases including the case r = 6 in the space of bilinear maps C × C → C. This space of bilinear maps includes the matrix multiplication operator M2 for two by two matrices. We show these newly obtained polynomials do not vanish on the matrix ...

We utilize the Bellman function technique to prove a bilinear dimension-free inequality for the Hermite operator. The Bellman technique is applied here to a non-local operator, which at first did not seem to be feasible. As a consequence of our bilinear inequality one proves dimension-free boundedness for the Riesz-Hermite transforms on L with linear growth in terms of p. A feature of the proof...