The consideration of tensor products of 0-Hecke algebra modules leads to natural analogs of the Bessel J-functions in the algebra of noncommutative symmetric functions. This provides a simple explanation of various combinatorial properties of Bessel functions.

Multidimensional and matrix versions of the Yamada-Watanabe theorem are proved. They are applied to particle systems of squared Bessel processes and to matrix analogues of squared Bessel processes: Wishart and Jacobi matrix processes.

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

It is proved that stability multipliers such as Zames–Falb multipliers, Popov multipliers, and RL/RC multipliers, known to preserve positivity of monotone memoryless nonlinearities, do not, in general, preserve their incremental positivity. Our result implies that stability results based on these multipliers should be interpreted with caution since without incremental positivity the continuity ...

Multipliers are often used to find conditions for the absolute stability of Lur'e systems. They can be used either in conjunction with passivity theory or within the more recent framework of integral quadratic constraints (IQCs). This seminar presents two equivalence results within multiplier theory. In the first part of the seminar, passivity with multipliers and IQC theory are compared. The p...

The increasing demand for the high fidelity portable devices has laid emphasis on the development of low power and high performance systems. In the next generation processors, the low power design has to be incorporated into fundamental computation units, such as multipliers. The characterization and optimization of such low power multipliers will aid in comparison and choice of multiplier modu...

n this article, we prove an lp-lq-version of morgan’s theorem for the generalized bessel transform.

Non-diffracting Bessel beams, including zero-order and high-order Bessel Beams which carry orbital angular momentum (OAM), enable a variety of important applications in optical micromanipulation, sub-diffraction imaging, high speed photonics/quantum communication, etc. The commonly used ways to create Bessel beams, including an axicon or a digital hologram written to a spatial light modulator (...

A rigorous analysis of the unstable Bessel resonator with convex output coupler is presented. The Huygens-Fresnel self-consistency equation is solved to extract the first eigenmodes and eigenvalues of the cavity, taking into account the finite apertures of the mirrors. Attention was directed to the dependence of the output transverse profiles; the losses; and the modal-frequency changes on the ...

In this paper, the quaternion Bessel-Fourier moments are introduced. The significance of phase information in quaternion Bessel-Fourier moments is investigated and an accurate estimation method for rotation angle is described. Furthermore, a new set of invariant descriptors based on the magnitude and the phase information of quaternion Bessel-Fourier moments is derived. Experimental results sho...