In this paper, we generalize the windowed Fourier transform to the windowed linear canonical transform by substituting the Fourier transform kernel with the linear canonical transform kernel in the windowed Fourier transform definition. It offers local contents, enjoys high resolution, and eliminates cross terms. Some useful properties of the windowed linear canonical transform are derived. Tho...

In practical engineering, small-scale data sets are usually sparse and contaminated by noise. In this paper, we propose a new sequence of orthogonal polynomials varying with their coefficient, unified Chebyshev polynomials (UCP), which has two important properties, namely, orthogonality and adaptivity. Based on these new polynomials, a new kernel function, the unified Chebyshev kernel (UCK), is...

Abstract This paper introduces a novel framework for generative models based on Restricted Kernel Machines (RKMs) with joint multi-view generation and uncorrelated feature learning, called Gen-RKM. To enable generation, this mechanism uses shared representation of data from various views. Furthermore, the model has primal dual formulation to incorporate both kernel-based (deep convolutional) ne...

Abstract-A half-range orthogonality theorem concerning the established elementary solutions of the two-group neutron transport equation for isotropic scattering and plane geometry is proved. The orthogonality relations are based on a Chandrasekhar-type H-matrix, and all necessary normalization integrals are evaluated so that the desired expansion coefficients may be expressed concisely in terms...

‎In this paper‎, ‎we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$‎. ‎We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator‎. ‎Also‎, ‎we prove that every compact normal operator is a strongly orthogo...

In 2003, Araujo and Jarosz showed that every bijective linear map θ : A → B between unital standard operator algebras preserving zero products in two ways is a scalar multiple of an inner automorphism. Later in 2007, Zhao and Hou showed that similar results hold if both A,B are unital standard algebras on Hilbert spaces and θ preserves range or domain orthogonality. In particular, such maps are...

We study orthogonal polynomials with periodically modulated Jacobi parameters in the case when 0 lies on soft edge of spectrum corresponding periodic matrix. determine orthogonality measure is absolutely continuous and we provide a constructive formula for it terms limit Turán determinants. next consider asymptotics solutions associated second order difference equation. Finally, scaling limits ...

In this paper, the notion of rank-k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for ϵ > 0; the notion of Birkhoff-James approximate orthogonality sets for ϵ-higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed denitions yield a natural genera...

We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform (CWFT). Based on the spectral representation of the Clifford Fourier transform (CFT), we derive several important properties such as shift, modulation, reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to ...