Orthogonal Familes of Real Sequences
نویسندگان
چکیده
It was already known that there exists a family of continuum many pairwise orthogonal elements of R. A family F ⊆ R \ 0 of pairwise orthogonal sequences is orthogonally complete or a maximal orthogonal family iff the only element of R orthogonal to every element of F is 0, the constant 0 sequence. It is somewhat surprising that Kunen’s perfect set of orthogonal elements is maximal (a fact first asserted by Abian). MAD families, nonprincipal ultrafilters, and many other such maximal objects cannot be even Borel.
منابع مشابه
Bessel Subfusion Sequences and Subfusion Frames
Fusion frames are a generalized form of frames in Hilbert spaces. In the present paper we introduce Bessel subfusion sequences and subfusion frames and we investigate the relationship between their operation. Also, the definition of the orthogonal complement of subfusion frames and the definition of the completion of Bessel fusion sequences are provided and several results related with these no...
متن کاملOn Generalization of Sturm-Liouville Theory for Fractional Bessel Operator
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...
متن کاملFast Periodic Auto and Cross Correlation Algorithms for an Orthogonal Set of Real-Valued Perfect Sequences from the Huffman Sequence
A perfect sequence has the optimal periodic autocorrelation function where all out-of-phase values are zero, and an orthogonal set has orthogonality that the periodic correlation function for any pair of distinct sequences in the set takes zero at the zero shift. The real-valued perfect sequences of period N = 2 are derived from a real-valued Huffman sequence of length 2 + 1 with ν ≥ n whose ou...
متن کاملComparison of the Gamma kernel and the orthogonal series methods of density estimation
The standard kernel density estimator suffers from a boundary bias issue for probability density function of distributions on the positive real line. The Gamma kernel estimators and orthogonal series estimators are two alternatives which are free of boundary bias. In this paper, a simulation study is conducted to compare small-sample performance of the Gamma kernel estimators and the orthog...
متن کاملContractive gauge functions in strongly orthogonal metric spaces
Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Symb. Log.
دوره 63 شماره
صفحات -
تاریخ انتشار 1998