A set with no Riesz basis of exponentials

نویسندگان

چکیده

We show that there exists a bounded subset of $\mathbb{R}$ such no system exponentials can be Riesz basis for the corresponding Hilbert space. An additional result gives lower bound constant any putative two dimensional disk.

برای دانلود باید عضویت طلایی داشته باشید

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Riesz Basis of Exponentials for a Union of Cubes in R

We extend to several dimensions the result of K. Seip and Y.I. Lyubarskii that proves the existence of Riesz basis of exponentials for a finite union of intervals with equals lengths.

متن کامل

Non-symmetric convex domains have no basis of exponentials

A conjecture of Fuglede states that a bounded measurable set Ω ⊂ R, of measure 1, can tile R by translations if and only if the Hilbert space L(Ω) has an orthonormal basis consisting of exponentials eλ(x) = exp2πi〈λ, x〉. If Ω has the latter property it is called spectral. We generalize a result of Fuglede, that a triangle in the plane is not spectral, proving that every non-symmetric convex dom...

متن کامل

Uniform Partitions of Frames of Exponentials into Riesz Sequences

The Feichtinger Conjecture, if true, would have as a corollary that for each set E ⊂ T and Λ ⊂ Z, there is a partition Λ1, . . . ,ΛN of Z such that for each 1 ≤ i ≤ N , {exp(2πixλ) : λ ∈ Λi} is a Riesz sequence. In this paper, sufficient conditions on sets E ⊂ T and Λ ⊂ R are given so that {exp(2πixλ)1E : λ ∈ Λ} can be uniformly partitioned into Riesz sequences.

متن کامل

Exponentials form a basis of discrete holomorphic functions

We show that discrete exponentials form a basis of discrete holomorphic functions. On a convex, the discrete polynomials form a basis as well.

متن کامل

Riesz Basis Property of Timoshenko Beams with Boundary Feedback Control

A Timoshenko beam equation with boundary feedback control is considered. By an abstract result on the Riesz basis generation for the discrete operators in the Hilbert spaces, we show that the closed-loop system is a Riesz system, that is, the sequence of generalized eigenvectors of the closed-loop system forms a Riesz basis in the state Hilbert space. 1. Introduction. The boundary feedback stab...

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

ژورنال

عنوان ژورنال: Revista Matematica Iberoamericana

سال: 2023

ISSN: ['2235-0616', '0213-2230']

DOI: https://doi.org/10.4171/rmi/1411