On the Riesz basis property of root vectors system for 2 × 2 Dirac type operators
نویسندگان
چکیده
منابع مشابه
On the Basis Property for the Root Vectors of Some Nonselfadjoint Operators*
M here and in the sequel denotes various constants, and 1 ?“I the norm of operator T on H. Under assumptions (1 ), (2) the operator A = L + T has a discrete spectrum, that is, every point of its spectrum is an eigenvalue of tinite algebraic multiplicity. If 1 is an eigenvalue of A, then the linear hull of the corresponding eigenvectors is called the eigenspace corresponding to d. Let h, be an e...
متن کاملBari–Markus property for Riesz projections of 1D periodic Dirac operators
The Dirac operators Ly = i 1 0 0 −1 dy dx + v(x)y, y = y1 y2 , x ∈ [0, π], with L 2-potentials v(x) = 0 P (x) Q(x) 0 , P,Q ∈ L 2 ([0, π]), considered on [0, π] with periodic, antiperiodic or Dirichlet boundary conditions (bc), have discrete spectra, and the Riesz projections SN = 1 2πi |z|=N− 1 2 (z − L bc) −1 dz, Pn = 1 2πi |z−n|= 1 2 (z − L bc) −1 dz are well-defined for |n| ≥ N if N is suffi...
متن کاملSome Sharp L 2 Inequalities for Dirac Type Operators ⋆
Sobolev and Hardy type inequalities play an important role in many areas of mathematics and mathematical physics. They have become standard tools in existence and regularity theories for solutions to partial differential equations, in calculus of variations, in geometric measure theory and in stability of matter. In analysis a number of inequalities like the Hardy–Littlewood– Sobolev inequality...
متن کاملOn the Hyponormal Property of Operators
Let $T$ be a bounded linear operator on a Hilbert space $mathscr{H}$. We say that $T$ has the hyponormal property if there exists a function $f$, continuous on an appropriate set so that $f(|T|)geq f(|T^ast|)$. We investigate the properties of such operators considering certain classes of functions on which our definition is constructed. For such a function $f$ we introduce the $f$-Aluthge tran...
متن کاملStability and Riesz Basis Property for General Network of Strings
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,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2016
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2016.03.085