منابع مشابه
Uniqueness of Dilation Invariant Norms
Let δa be a nontrivial dilation. We show that every complete norm ‖ · ‖ on L1(RN ) that makes δa from (L1(RN ), ‖ · ‖) into itself continuous is equivalent to ‖ · ‖1. δa also determines the norm of both C0(R ) and Lp(RN ) with 1 < p < ∞ in a weaker sense. Furthermore, we show that even all the dilations do not determine the norm on L∞(RN ).
متن کاملReparametrization Invariant Norms
This paper explores the concept of reparametrization invariant norm (RPI-norm) for C1-functions that vanish at −∞ and whose derivative has compact support, such as C1 c -functions. An RPI-norm is any norm invariant under composition with orientation-preserving diffeomorphisms. The L∞-norm and the total variation norm are well-known instances of RPI-norms. We prove the existence of an infinite f...
متن کاملInequalities for unitarily invariant norms
This paper aims to discuss some inequalities for unitarily invariant norms. We obtain several inequalities for unitarily invariant norms.
متن کاملStationary flows and uniqueness of invariant measures
In this short paper, we consider a quadruple (Ω,A , θ, μ), where A is a σ-algebra of subsets of Ω, and θ is a measurable bijection from Ω into itself that preserves the measure μ. For each B ∈ A , we consider the measure μB obtained by taking cycles (excursions) of iterates of θ from B. We then derive a relation for μB that involves the forward and backward hitting times of B by the trajectory ...
متن کاملLocal Uniqueness of the Circular Integral Invariant
This article is concerned with the representation of curves by means of integral invariants. In contrast to the classical differential invariants they have the advantage of being less sensitive with respect to noise. The integral invariant most common in use is the circular integral invariant. A major drawback of this curve descriptor, however, is the absence of any uniqueness result for this r...
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: Proceedings of the American Mathematical Society
سال: 2004
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-04-07327-7