Clifford Fourier-Mellin transform with two real square roots of -1 in Cl(p, q), p+q=2
نویسنده
چکیده
We describe a non-commutative generalization of the complex Fourier-Mellin transform to Clifford algebra valued signal functions over the domain Rp,q taking values in Cl(p,q), p+q = 2.
منابع مشابه
The Clifford Fourier transform in real Clifford algebras
We use the recent comprehensive research [17, 19] on the manifolds of square roots of −1 in real Clifford’s geometric algebras Cl(p,q) in order to construct the Clifford Fourier transform. Basically in the kernel of the complex Fourier transform the imaginary unit j ∈ C is replaced by a square root of−1 in Cl(p,q). The Clifford Fourier transform (CFT) thus obtained generalizes previously known ...
متن کاملQuaternionic Fourier-Mellin Transform
In this contribution we generalize the classical Fourier Mellin transform [3], which transforms functions f representing, e.g., a gray level image defined over a compact set of R. The quaternionic Fourier Mellin transform (QFMT) applies to functions f : R → H, for which |f | is summable over R+ × S under the measure dθ dr r . R ∗ + is the multiplicative group of positive and non-zero real numbe...
متن کاملExplicit isomorphisms of real Clifford algebras
It is well known that the Clifford algebra Cl p,q associated to a nondegenerate quadratic form on R n (n = p + q) is isomorphic to a matrix algebra K(m) or direct sum K(m) ⊕ K(m) of matrix algebras, where K = R, C, H. On the other hand, there are no explicit expressions for these isomorphisms in literature. In this work, we give a method for the explicit construction of these isomorphisms. Let ...
متن کاملOn Bilinear Littlewood-paley Square Functions
On the real line, let the Fourier transform of kn be k̂n(ξ) = k̂(ξ−n) where k̂(ξ) is a smooth compactly supported function. Consider the bilinear operators Sn(f, g)(x) = ∫ f(x + y)g(x − y)kn(y) dy. If 2 ≤ p, q ≤ ∞, with 1/p + 1/q = 1/2, I prove that ∞ ∑ n=−∞ ‖Sn(f, g)‖2 ≤ C‖f‖p‖g‖q . The constant C depends only upon k.
متن کاملQuadratic Reciprocity and the Sign of the Gauss Sum via the Finite Weil Representation
We give new proofs of two basic results in number theory: The law of quadratic reciprocity and the sign of the Gauss sum. We show that these results are encoded in the relation between the discrete Fourier transform and the action of the Weyl element in the Weil representation modulo p, q and pq. 0. Introduction Two basic results due to Gauss are the quadratic reciprocity law and the sign of th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1306.1679 شماره
صفحات -
تاریخ انتشار 2013