Fourier analysis on finite abelian groups
نویسنده
چکیده
[2] The notation L(G) is meant to suggest the presence of the inner product on this space of functions. On a general space X with an integral, the iner product is 〈f1, f2〉 = ∫ X f1f 2. [3] The term character has different meanings in different contexts. The simplest sense is a group homomorphism to C×. However, an equally important use is for the trace of a group homomorphism ρ : G → GLn(k) from G to invertible n-by-n matrices with entries in a field k. In the latter sense,
منابع مشابه
Quantum Error-Correction Codes on Abelian Groups
We prove a general form of bit flip formula for the quantum Fourier transform on finite abelian groups and use it to encode some general CSS codes on these groups.
متن کاملHarmonic Analysis on Finite Abelian Groups
We give a discussion of harmonic analysis on finite abelian groups, emphasizing various ways in which the structure of the group is encoded on various spaces of functions, ways in which the Fourier transform detects and preserves these structures. We discuss the major tools, like convolutions and Fourier transforms, along with some fundamental theorems, like the Plancheral, Parseval, Fourier in...
متن کاملFinite Fourier Analysis and Dirichlet’s Theorem
This is an expository paper on finite Fourier analysis and basic number theory. The focus of the paper is finite Abelian groups and the properties of these groups which are used in the proof of the Dirichlet prime number theorem. We then introduce the specific elements and basic structure of the proof of Dirichlet’s theorem.
متن کاملControl/target Inversion Property on Abelian Groups
We show that the quantum Fourier transform on finite fields used to solve query problems is a special case of the usual quantum Fourier transform on finite abelian groups. We show that the control/target inversion property holds in general. We apply this to get a sharp query complexity separation between classical and quantum algorithms for a hidden homomorphism problem on finite abelian groups.
متن کاملFourier analysis on finite Abelian groups: some graphical applications
A survey of basic techniques of Fourier analysis on a finite Abelian group Q with subsequent applications in graph theory. In particular, evaluations of the Tutte polynomial of a graph G in terms of cosets of the Q-flows (or dually Q-tensions) of G. Other applications to spanning trees of Cayley graphs and group-valued models on phylogenetic trees are also used to illustrate methods.
متن کاملOn the Finite Groups that all Their Semi-Cayley Graphs are Quasi-Abelian
In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.
متن کامل