Stability and Riesz Basis Property for General Network of Strings

نویسندگان

  • YAN NI GUO
  • QI XU
چکیده

In this paper, we study the generation problem of Riesz basis for a general network of strings with joint damping at each vertex. First, we give a basic spectral property of the system operator A. Under certain conditions, we prove that the spectrum of A is distributed in a strip parallel to the imaginary axis. By the discussion of the completeness of generalized eigenvectors of the operator A, we prove further that there exists a sequence of generalized eigenvectors of A that forms a Riesz basis with parentheses in the Hilbert state space.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

New characterizations of fusion bases and Riesz fusion bases in Hilbert spaces

In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hil...

متن کامل

The Riesz basis property of a Timoshenko beam with boundary feedback and application

The Riesz basis property of the generalized eigenvector system of a Timoshenko beam with boundary feedback is studied. Firstly, two auxiliary operators are introduced, and the Riesz basis property of their eigenvector systems is proved. This property is used to show that the generalized eigenvector system of a Timoshenko beam with some linear boundary feedback forms a Riesz basis in the corresp...

متن کامل

On Spectrum of a General Petrovsky Type Equation and Riesz Basis of N-connected Beams with Linear Feedback at Joints

A framework of a general type of Petrovsky equation is formulated. The characteristic equation for eigenvalues of the system is derived and the associated eigenfunctions are found. For N connected beams with linear feedbacks at joint points, the asymptotic expansions of eigenvalues and eigenfunctions are further developed, and the Riesz basis property and the exponential stability are then conc...

متن کامل

Spectrum and dynamical behavior of a kind of planar network of non-uniform strings with non-collocated feedbacks

A kind of planar network of strings with non-collocated terms in boundary feedback controls is considered. Suppose that the network is constituted by n non-uniform strings, connected by one vibrating point mass. The displacements of these strings are continuous at the common vertex. The noncollocated terms are contained in feedback controls at exterior nodes. The well-posedness of the correspon...

متن کامل

A 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 کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009