Radon–Nikodym Property and Area Formula for Banach Homogeneous Group Targets

fixed point property for banach algebras associated to locally compact groups

در این پایان نامه به بررسی خاصیت نقطه ثابت و خاصیت نقطه ثابت برای نیم گروههای برگشت پذیر چپ روی بعضی جبرهای باناخ از جمله جبر فوریه و جبر فوریه استیلتیس پرداخته شده است. برای مثال بیان شده است که اگر گروه یک گروه فشرده موضعی با همسایگی فشرده برای عنصر همانی که تحت درونریختی ها پایاست باشد آنگاه جبر فوریه و جبر فوریه استیلتیس دارای خاصیت نقطه ثابت برای نیم گروه های برگشت پذیر چپ است اگر و تنها ا...

The ¿-norm Extension Property for Banach Spaces1

A Combinatorial Formula for Homogeneous Moments

We refer to quantities such as the integrals in the left-hand side of (1) and (3) as homogeneous moments (in the given functions J1, . . . , Jn). For applications, we have in mind that M should be a compact smooth manifold equipped with a volume form and that J1, J2, . . . , Jn should be smooth functions. A simple example may be given by taking M = Sn−1 with its usual round metric and J1, J2, ....

The reconstruction formula for Banach frames and duality

We study conditions on a Banach frame that ensures the validity of a reconstruction formula. In particular, we show that any Banach frames for (a subspace of) Lp or Lp,q (1 ≤ p <∞) with respect to a solid sequence space always satisfies an unconditional reconstruction formula. The existence of reconstruction formulae allows us to prove some James-type results for atomic decompositions: an uncon...

Homogeneous Approximation Property for Wavelet Frames

The homogeneous approximation property (HAP) is useful in practice since it means that the number of building blocks involved in a reconstruction of f up to some error is essentially invariant under time-scale shifts. In this paper, we prove the HAP for a large class of wavelet frames which are generated with arbitrary time-scale shifts and wavelet functions satisfying moderate decaying conditi...