The Dirichlet ring and unconditional bases in L 2[0, 2π]

Signals generated in memristive circuits

“…The construction below follows the method established in [24] and [26], and will only be outlined. First, consider the set { ( )}, = 1 2 , as a candidate for a basis in H h .…”

“…These facts form the precepts of a new method of signal analysis which is numerically efficient and customizable to specific nano-circuits. Moreover, the method presented in [26] allows for a construction of a broad family of fast-transform bases, going beyond the framework of DAEP. Indeed, the paper identifies verifiable sufficient conditions on ( ) for the collection { ( )}, = 1 2 3 to be a Riesz basis.…”

“…We emphasize that ( ) need not necessarily descend from a DAEP. However, it is demonstrated in [26] that the bases arising from the specific DAEP considered in [24] are in fact Riesz. The Riesz property is of interest from the point of view of applications as it guaranties numerically stable decomposition of a signal in the given basis.…”

“…This becomes a hindrance when one wishes to carry out, say, signal denoising or compression in a way that does not spoil the hysteretic features. Section 3 outlines an approach to this problem, which utilizes a novel fast transform, [24][25][26]. The discussion culminates in Section 4, where we argue that hysteretic distortion may also be simulated by certain fast transforms.…”

Complexity in Mathematics and Complexity of a Physical Process

“…The high complexity of the zeta is the very reason it does not admit a simple description such as a differential-algebraic equation would supply. However, loosely speaking, one may view the Dirichlet series whose most or even all a n ≠ 0 as nontrivial operators in a Hilbert space, [2]. Some of those operators will be related to special bases in the Hilbert space which in turn may, but need not to, stem from a differential algebraic eigenvalue problem.…”