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Linear ordinary differential equations: revisiting the impulsive response method using factorization
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A fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization
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The spherical Paley-Wiener theorem on the complex Grassmann manifolds SU(p+q)/S(U(p)times U(q))
No full textWe prove the Paley-Wiener theorem for the spherical transform on the complex Grassmann manifolds U/K=\mbox{SU}(p+q)/\mbox{S}(\mbox{U}_p\times \mbox{U}_q). This theorem characterizes the -biinvariant smooth functions on the group that are supported in the -invariant ball of radius , with less than the injectivity radius of , in terms of holomorphic extendability, exponential growth, and Weyl invariance properties of the spherical Fourier transforms , originally defined on the discrete set \L_{sph} of highest restricted spherical weight
Harmonic Analysis for Spinor Fields in Complex Hyperbolic Spaces
No full textAbstractL2 harmonic analysis for Dirac spinors on the complex hyperbolic space Hn(C) is developed. The spinor spherical functions are calculated in terms of Jacobi functions. The Plancherel and Paley–Wiener theorems for the spherical transform are obtained by reduction to Jacobi analysis. We demonstrate analytically the existence of harmonic L2 spinors in the case of n even. The action of the invariant differential operators on the Poisson transforms is given explicitly
An Introduction to Linear Ordinary Differential Equations Using the Impulsive Response Method and Factorization
No full textThis book presents a method for solving linear ordinary differential equations based on the factorization of the differential operator. The approach for the case of constant coefficients is elementary, and only requires a basic knowledge of calculus and linear algebra. In particular, the book avoids the use of distribution theory, as well as the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The case of variable coefficients is addressed using Mammana’s result for the factorization of a real linear ordinary differential operator into a product of first-order (complex) factors, as well as a recent generalization of this result to the case of complex-valued coefficients
The υ-radial paley-wiener theorem for the helgason fourier transform on damek-ricci spaces
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