We establish an L2×L2 to L estimate for the bilinear Hilbert transform along a curve defined by a monomial. Our proof is closely related to multilinear oscillatory integrals.

In this work, a new on-line method for detecting incipient failures in electrical motors is proposed.The method is based on monitoring certain statistical parameters estimated from the analysis of the steady state stator current (for broken bars, saturation, eccentricities, and bearing failures) or the axial flux signal (for coil short-circuits in the stator windings). The approach is based on ...

This work presents a novel rotational invariant quadrature filter approach called the conformal monogenic signal for analyzing i(ntrinsic)1D and i2D local features of any curved 2D signal such as lines, edges, corners and junctions without the use of steering. The conformal monogenic signal contains the monogenic signal as a special case for i1D signals and combines monogenic scale space, phase...

It is shown that the bilinear Hilbert transforms Hα,β(f, g)(x) = p.v. Z R f(x− αt)g(x− βt) dt t map L1(R)×L2(R)→ L(R) uniformly in the real parameters α, β when 2 < p1, p2 <∞ and 1 < p = p1p2 p1+p2 < 2. Combining this result with the main result in [9], it follows that the operators H1,α map L (R) × L∞(R) → L(R) uniformly in the real parameter α ∈ [0, 1], as conjectured by A. Calderón.

where P(s, t) is a polynomial in s and t with P(0,0)= 0, and ∇P(0,0)= 0. We call H the (local) double Hilbert transform along the surface (s, t,P (s, t)). The operator may be precisely defined for a Schwartz function f by integrating where ≤ |s| ≤ 1 and η ≤ |t | ≤ 1, and then taking the limit as ,η→ 0. The corresponding 1-parameter problem has been extensively studied (see [RS1], [RS2], and [S]...

We continue the investigation initiated in [8] of uniform L bounds for the family of bilinear Hilbert transforms Hα,β(f, g)(x) = p.v. ∫ R f(x − αt)g(x − βt) dt t . In this work we show that Hα,β map L1(R) × L2(R) into L(R) uniformly in the real parameters α, β satisfying | β − 1| ≥ c > 0 when 1 < p1, p2 < 2 and 2 3 < p = p1p2 p1+p2 < ∞. As a corollary we obtain L × L∞ → L uniform bounds in the ...

Turbochargers are most widely used in automotive, marine and locomotive applications with diesel engines. To increase the engine performance nowadays, in aerospace applications also turbochargers are used. Mostly the turbocharger rotors are commonly supported over the fluid film bearings. With the operation, lubricant properties continuously alter leading to different load bearing capacities. T...

In this paper we display a family of Gaussian processes, with explicit formulas and transforms. This is presented the use duality tools in such way that corresponding path-space measures are mutually singular. We make representations canonical commutation relations (CCR) an infinite number degrees freedom. A key feature our construction for associated transforms; these infinite-dimensional anal...

Convergence of certain transforms of Markov processes generators implies large deviations. In this article, we apply abstract theorems of such type to stochastic evolution equations in real separable Hilbert space, giving diierent perspectives and extensions to some known results. When the drift term is semilinear, the rate function is explicitly identiied. The main large deviation theorem 18 3...