Mohammad Reza Mardanbeigi

Islamic Azad University Tehran Science and Research Branch | SRBIAU · Department of Mathematics

For every frame spectral measure µ, there exists a discrete measure ν as a frame measure. If µ is not a frame spectral measure, then there is not any general statement about the existence of frame measures ν for µ. This motivated us to examine Bessel and frame measures. We construct infinitely many measures µ which admit frame measures ν, and we sh...

‎Considering a finite Borel measure ‎$‎‎‎\mu‎$‎ on $\mathbb{R}^d‎$‎, a pair of conjugate exponents ‎$‎p, q‎$‎, and a compatible‎ semi-inner product on ‎$‎L^p(‎\mu‎)‎$‎, we have introduced (p, q)-Bessel and (p, q)-frame measures as a generalization of‎ the concepts of Bessel and frame measures. In addition, we have defined the notions of q-Bessel se...

Approximately dual frames as a generalization of duality notion in Hilbert spaces have applications in Gabor systems, wavelets, coorbit theory and sensor modeling. In recent years, the computing of the associated deviations of the canonical and alternate dual frames from the original ones has been considered by some authors. However, the quantitati...

Considering a finite Borel measure $ \mu $ on $ \mathbb{R}^d $, a pair of conjugate exponents $ p, q $, and a compatible semi-inner product on $ L^p(\mu) $, we introduce $ (p,q) $-Bessel and $ (p,q) $-frame measures as a generalization of the concepts of Bessel and frame measures. In addition, we define notions of $ q $-Bessel and $ q$-frame in the...

We investigate σ -approximate contractibility and σ -approximate amenability of Banach algebras, which are extensions of usual notions of contractibility and amenability, respectively, where σ is a dense range or an idempotent bounded endomorphism of the corresponding Banach algebra.

Let S and T be semigroups and S◊T be a Zappa product. Let F be a C -algebra of bounded continuous complex-valued functions on S◊T (Zappa). Necessary and sucient conditions are given for the F-compactification of S ◊T (Zappa)to be