A Method for Generating Infinite Positive Self-adjoint Test Matrices and Riesz Bases
نویسندگان
چکیده
In this article we propose a method to easily generate infinite multi-index positive definite self-adjoint matrices as well as Riesz bases in suitable subspaces of L2(Rd). The method is then applied to obtain some classes of multi-index Toeplitz matrices which are bounded and strictly positive on 2(Zd). The condition number of some of these matrices is also computed.
منابع مشابه
Matrix Representation of Operators Using Frames
In this paper it is investigated how to find a matrix representation of operators on a Hilbert space H with Bessel sequences, frames and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs). Therefore it is useful to extend the known method of matrix representation by using these sequences instead of ONBs for these application areas. We will give ba...
متن کاملMatrix Representation of Bounded Linear Operators By Bessel Sequences, Frames and Riesz Sequence
In this work we will investigate how to find a matrix representation of operators on a Hilbert space H with Bessel sequences, frames and Riesz bases as an extension of the known method of matrix representation by ONBs. We will give basic definitions of the functions connecting infinite matrices defining bounded operators on l and operators onH. We will show some structural results and give some...
متن کاملA New Approach to Continuous Riesz Bases
This paper deals with continuous frames and continuous Riesz bases. We introduce continuous Riesz bases and give some equivalent conditions for a continuous frame to be a continuous Riesz basis. It is certainly possible for a continuous frame to have only one dual. Such a continuous frame is called a Riesz-type frame [13]. We show that a continuous frame is Riesz-type if and only if it is a con...
متن کاملOn duality of modular G-Riesz bases and G-Riesz bases in Hilbert C*-modules
In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...
متن کاملFrames, Riesz Bases and Double Infinite Matrices
In this paper we have used double infinite matrix A = (ailjk) of real numbers to define the A-frame. Some results on Riesz basis and A-frame also have been studied. This Work is motivated from the work of Moricz and Rhoades [7]. 2001 AMS Classification. Primary 41A17, Secondary 42C15.
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:
- SIAM J. Matrix Analysis Applications
دوره 26 شماره
صفحات -
تاریخ انتشار 2005