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We show that non of the spaces ( ⊕∞ n=1 lp)lq , 1 ≤ p ̸= q < ∞ have a greedy basis. This solves a problem raised by Dilworth, Freeman, Odell and Schlumprect. Similarly, the spaces ( ⊕∞ n=1 lp)c0 , 1 ≤ p < ∞, and ( ⊕∞ n=1 co)lq , 1 ≤ q < ∞, do not have greedy bases. It follows from that and known results that a class of Besov spaces on Rn lack greedy bases as well.

The multiresolution expansion {Ejf}j∈N, f ∈ D Lq (R), 1 ≤ q ≤ ∞, is defined via a scaling function which order of regularity is equal to the order of f. Abelian and Tauberian type theorems for the quasiasymptotic behavior at infinity of distributions from D Lq (R) related to the quasiasymptotic behavior at infinity of its projections Ejf, j ∈ N, are given. AMS Mathematics Subject Classification...

We show that a reflexive subspace of the predual of a von Neumann algebra embeds into a noncommutative Lp space for some p > 1. This is a noncommutative version of Rosenthal’s result for commutative Lp spaces. Similarly for 1 ≤ q < 2, an infinite dimensional subspace X of a noncommutative Lq space either contains lq or embeds in Lp for some q < p < 2. The novelty in the noncommutative setting i...

Pertumbuhan ekonomi yang tinggi wujud salah satu bentukkeberhasilan pembangunan suatu daerah. Pembangunan daerahdapat berkembang melalui pengembangan sektor unggulan daerahyang akan mendorong berkembangnya lainnya. Tujuan daripenelitian ini ialah untuk mengidentifikasi perekonomian yangmerupakan basis dan non di Kota Metro denganmenggunakan metode location quotient (LQ) dynamic locationquotient...

This paper is concerned with a discrete-time indefinite stochastic LQ problem in an infinite-time horizon. A generalized stochastic algebraic Riccati equation GSARE that involves the MoorePenrose inverse of a matrix and a positive semidefinite constraint is introduced. We mainly use a semidefinite-programmingSDPbased approach to study corresponding problems. Several relations among SDP compleme...

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E-mail: [email protected] Abstract: We determine the exact order of the p-average linear n-widths λ n (W r 2 , μ, Lq)p, 1 ≤ q < ∞, 0 < p <∞, of the Sobolev space W r 2 equipped with a Gaussian measure μ in the Lq-norm. Moreover, we also calculate the probabilistic linear (n, δ)-widths and p-average linear n-widths of the finitedimensional space R with the standard Gaussian measure in l q , i.e.,

In this paper we construct an infinite horizon LQ optimal controller for a linear stationary differential-algebraic equation (DAE) and prove that stabilizability from the given initial state is necessary and sufficient for the controller existence. We also solve the problem of finite horizon LQ optimal control. Our approach is based on ideas from linear geometric control theory that allows one ...