A novel and eective method based on Haar wavelets and Block Pulse Functions(BPFs) is proposed to solve nonlinear Fredholm integro-dierential equations of fractional order.The operational matrix of Haar wavelets via BPFs is derived and together with Haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. Our new met...

We introduce a non standard but to our opinion natural order on the initial segments of the Haar system and investigate the isomorphic classi cation of the linear span in Lp of block bases with respect to this order Introduction In DS it was proved that every unconditional basic sequence fxig i in Lp p which is not equivalent to the natural basis of p has the property that for some K and every ...

this paper presents a proof of stirling's formula using haar wavelets and some properties of hilbert space, such as parseval's identity. the present paper shows a connection between haar wavelets and certain sequences.

A novel and effective method based on Haar wavelets and Block Pulse Functions (BPFs) is proposed to solve nonlinear Fredholm integro-differential equations of fractional order. The operational matrix of Haar wavelets via BPFs is derived and together with Haar wavelet operational matrix of fractional integration are used to transform the mentioned equation to a system of algebraic equations. Our...

Footprint identification is the measurement of footprint features for recognizing the identity of a user. Footprint is universal, easy to capture and does not change much across time. Footprint biometric system does not require specialized acquisition devices. Footprint image of a left leg is captured for hundred people in different angles. No special lighting is used in this setup. The foot im...

The Euclidean group (Rn,+) where (n?N, plays a key role in harmonic analysis. If we consider the Lebesgue measure ()nd?xR as the Haar measure of this group then 12(2)()nd?x=d?RR. In this article we look for LCA groups K, whose Haar measures have a similar property. In fact we will show that for some LCA groups K with the Haar measure K?, there exists a constant such that 0KC>()(2)KKK?A=C?A for ...

We characterize the Schauder and unconditional basis properties for Haar system in Triebel–Lizorkin spaces $$F^s_{p,q}({{\mathbb {R}}}^d)$$ , at endpoint cases $$s=1$$ $$s=d/p-d$$ $$p=\infty $$ . Together with earlier results Garrigós et al. (J Fourier Anal Appl 24(5):1319–1339, 2018) Seeger Ullrich (Math Z 285:91–119, 2017), this completes picture such scale, complements a similar study Besov ...