We establish an L×L → L norm estimate for a bilinear oscillatory integral operator along parabolas incorporating oscillatory factors e −β .

In this work we prove Hardy space estimates for bilinear Littlewood-Paley-Stein square function and Calderón-Zygmund operators. Sufficient Carleson measure type conditions are given for square functions to be bounded from H p1 ×H p2 into Lp for indices smaller than 1, and sufficient BMO type conditions are given for a bilinear Calderón-Zygmund operator to be bounded from H p1 ×H p2 into H p for...

In this paper the notion of an M -th order invariant bilinear differential pairing is introduced and a formal definition is given. If the manifold has an AHS structure, then various first order pairings are constructed. This yields a classification of all first order invariant bilinear differential pairings on homogeneous spaces with an AHS structure except for certain totally degenerate cases....

For the Kac-Wakimoto hierarchy constructed from the principal vertex operator realization of the basic representation of the affine Lie algebra D (1) n , we compute the coefficients of the corresponding Hirota bilinear equations, and verify the coincidence of these bilinear equations with the ones that are satisfied by Givental’s total descendant potential of the Dn singularity, as conjectured ...

Abstract. We prove old and new L bounds for the quartile operator, a Walsh model of the bilinear Hilbert transform, uniformly in the parameter that models degeneration of the bilinear Hilbert transform. We obtain the full range of exponents that can be expected from known bounds in the degenerate and non-degenerate cases. For the new estimates with exponents p close to 1 the argument relies on ...

The diagonalization of the Heun–Racah operator is studied with help modified algebraic Bethe ansatz. This most general bilinear expression in two generators Racah algebra. A presentation this algebra given terms dynamical operators and allows construction vectors for operator. associated equations are derived both homogeneous inhomogeneous cases.

For the Kac-Wakimoto hierarchy constructed from the principal vertex operator realization of the basic representation of the affine Lie algebra D (1) n , we compute the coefficients of the correspondent Hirota bilinear equations, and verify the coincidence of these bilinear equations with the ones that are satisfied by Givental’s total descendant potential of the Dn singularity, as conjectured ...

We study interpolation, generated by an abstract method of means, of bilinear operators between quasi-Banach spaces. It is shown that under suitable conditions on the type of these spaces and the boundedness of the classical convolution operator between the corresponding quasi-Banach sequence spaces, bilinear interpolation is possible. Applications to the classical real method spaces, Calderón-...

This paper is concerned with the numerical treatment of pseudo-diierential equations in I R 2 , employing wavelet Galerkin methods. We construct wavelet bases adapted to a given pseudo-diierential operator in the sense that functions on diierent reenement levels are orthogonal with respect to a certain bilinear form induced by the operator.

We present a unifying view of discrete-time operator models used in the context of finite word length linear signal processing. Comparisons are made between the recently presented gamma operator model, and the delta and rho operator models for performing nonlinear system identification and prediction using neural networks. A new model based on an adaptive bilinear transformation which generaliz...