Weak Greedy Algorithms and the Equivalence Between Semi-greedy and Almost Greedy Markushevich Bases

NON-EQUIVALENT GREEDY AND ALMOST GREEDY BASES IN `p

For 1 < p < ∞ and p 6= 2 we construct a family of mutually non-equivalent greedy bases in `p having the cardinality of the continuum. In fact, no basis from this family is equivalent to a rearranged subsequence of any other basis thereof. We are able to extend this statement to the spaces Lp and H1. Moreover, the technique used in the proof adapts to the setting of almost greedy bases where sim...

Weak greedy algorithms

Theoretical greedy type algorithms are studied: a Weak Greedy Algorithm, a Weak Orthogonal Greedy Algorithm, and a Weak Relaxed Greedy Algorithm. These algorithms are defined by weaker assumptions than their analogs the Pure Greedy Algorithm, an Orthogonal Greedy Algorithm, and a Relaxed Greedy Algorithm. The weaker assumptions make these new algorithms more ready for practical implementation. ...

Approximate Weak Greedy Algorithms

We present a generalization of V. Temlyakov’s weak greedy algorithm, and give a sufficient condition for norm convergence of the algorithm for an arbitrary dictionary in a Hilbert space. We provide two counter-examples to show that the condition cannot be relaxed for general dictionaries. For a class of dictionaries with more structure, we give a more relaxed necessary and sufficient condition ...

Greedy and Quasi-greedy Expansions in Non-integer Bases

We generalize several theorems of Rényi, Parry, Daróczy and Kátai by characterizing the greedy and quasi-greedy expansions in non-integer bases.

Greedy Algorithms