Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...

We obtain size estimates for the distribution function of the bilinear Hilbert transform acting on a pair of characteristic functions of sets of finite measure, that yield exponential decay at infinity and blowup near zero to the power −2/3 (modulo some logarithmic factors). These results yield all known L bounds for the bilinear Hilbert transform and provide new restricted weak type endpoint e...

The X s,b spaces, as used by Beals, Bourgain, Kenig-Ponce-Vega, Klainerman-Machedon and others, are fundamental tools to study the low-regularity behaviour of non-linear dispersive equations. It is of particular interest to obtain bilinear or multilinear estimates involving these spaces. By Plancherel's theorem and duality, these estimates reduce to estimating a weighted convolution integral in...

The X s,b spaces, as used by Beals, Bourgain, Kenig-Ponce-Vega, Klainerman-Machedon and others, are fundamental tools to study the low-regularity behaviour of non-linear dispersive equations. It is of particular interest to obtain bilinear or multilinear estimates involving these spaces. By Plancherel's theorem and duality, these estimates reduce to estimating a weighted convolution integral in...

as an application of hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. we have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear backlund transformations and construction of ...

The paper introduces a new autoregressive model of order one for time seriesof counts. is comprised linear as well bilinear component. These two components are governed by random coefficients. autoregression achieved using the negative binomial thinning operator. method moments and conditional maximum likelihood discussed parameter estimation. practicality presented on real data set.

Let L be the Lie algebra of a simple algebraic group defined over F and let H be a split Cartan subalgebra of L. Let R = (X,Φ, Y,Φ∨) be the root datum of L, so that H = Y ⊗ F, and let 〈·, ·〉 : Φ × Φ∨ 7→ Z be the corresponding bilinear form. This bilinear form induces a linear form on the roots of L by defining α : h 7→ P i〈α, yi〉ti, where h = P i yi⊗ ti. Given a root α, we define the multiplici...

The X s,b spaces, as used by Beals, Bourgain, Kenig-Ponce-Vega, Klainerman-Machedon and others, are fundamental tools to study the low-regularity behaviour of non-linear dispersive equations. It is of particular interest to obtain bilinear or multilinear estimates involving these spaces. By Plancherel's theorem and duality, these estimates reduce to estimating a weighted convolution integral in...

The endpoint Strichartz estimate ‖ef‖L2 t L x (R×R) . ‖f‖L2 x (R) is known to be false by the work of Montgomery-Smith [2], despite being only “logarithmically far” from being true in some sense. In this short note we show that (in sharp constrast to the Lpt,x Strichartz estimates) the situation is not improved by passing to a bilinear setting; more precisely, if P, P ′ are non-trivial smooth F...