منابع مشابه
-Regularized C-Resolvent Families: Regularity and Local Properties
and Applied Analysis 3 In the case k t t/Γ α 1 , where α > 0, and Γ · denotes the Gamma function, it is also said that R t t∈ 0,τ is an α-times integrated a,C -resolvent family; in such a way, we unify the notion of local α-times integrated C-semigroups a t ≡ 1 and cosine functions a t ≡ t 1, 13, 14 . Furthermore, in the case k t : ∫ t0K s ds, t ∈ 0, τ , where K ∈ Lloc 0, τ and K/ 0, we obtain ...
متن کاملOn Maximal Regularity and Semivariation of α-Times Resolvent Families*
Let and A be the generator of an -times resolvent family 1 α < < 2 α ( ) { } 0 t S t α ≥ on a Banach space X. It is shown that the fractional Cauchy problem , ( ) ( ) ( ) t u t Au t f t α = + D ( ] 0, t r ∈ ; has maximal regularity on ( ) ( 0 , u u′ ) ( ) 0 D A ∈ [ ] ( 0, ; C r ) X if and only if is of bounded semivariation on ( ) ⋅ Sα [ ] 0, r .
متن کاملSubscalar Operators and Growth of Resolvent
We construct a Banach space operator T which is not E(T)subscalar but ‖(T − z)−1‖ ≤ (|z| − 1)−1 for |z| > 1 and m(T − z) ≥ const · (1 − |z|)3 for |z| < 1 (here m denotes the minimum modulus). This gives a negative answer to a variant of a problem of Laursen and Neumann. We also give a sufficient condition (in terms of growth of resolvent and of an analytic left inverse of T − z) implying that T...
متن کاملNecessary and Sufficient Conditions for Almost Regularity of Uniform Birkhoff Interpolation Schemes
In this article, using a combination of the necessary and sufficient conditions for the almost regularity of an interpolation scheme, we will determine all plane uniform Birkhoff schemes, when the set of interpolated nodes has n elements and the set of derivatives we are interpolating with is )} 0 , 1 ( ), 0 , 0 {( = A . For the same A we will determine all rectangular Birkhoff uniform interpol...
متن کاملSelfsimilarity and Growth in Birkhoff Sums for the Golden Rotation
We study Birkhoff sums Sk(α) = ∑k j=1 Xj(α) with Xj(α) = g(jα) = log |2− 2 cos(2πjα)| at the golden mean rotation number α = ( √ 5 − 1)/2 with periodic approximants pn/qn. The summation of such quantities with logarithmic singularity is motivated by critical KAM phenomena. We relate the boundedness of log averaged Birkhoff sums Sk/ log(k) and the convergence of Sqn (α) with the existence of an ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2006
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2005.10.058