FP (g) = trgKerP − trgCokerP ∈ R(S) where R(S1) is the character ring of the S1-modules. We say that P is rigid with respect to this S1-action, if FP (g) is independent of g. Two well-known examples of rigid elliptic operators are the signature operator ds and the Dirac operator D [AH]. Now let L̃Spin(2l) denote the central extension of the loop group LSpin(2l) and E be a positive energy represe...

In structural design of steel frames, in order to achieve proper safety, the effect uncertainties and loading parameters structure must be considered. This approach is obtained by defining a reliability index. this study, Modified Dolphin Monitoring (MDM) operator was used evaluate index three well-known frame structures based on Hasofer-Lind method. The evaluated using EVPS VPS algorithms with...

We consider systems of vectors of the form {Ahi : i ∈ I, n ≥ 0} where {hi}i∈I is a countable (finite or infinite) system of vectors in a separable Hilbert space H and A ∈ B(H) is a bounded operator. We show that a system of that form can never be both complete and minimal, and find conditions that the operator A needs to satisfy for the system to be a frame or a complete Bessel system. We also ...

We describe the spectra and pseudospectra of continuous time and discrete time waveform relaxation operators. Since the spectrum of the finite-interval waveform relaxation operator is only a singleton, the spectrum of the infinite-interval operator is typically used to describe the behavior of waveform relaxation algorithms. Here, we show that the pseudospectrum is a more useful tool for analyz...

In this paper, we first discuss about canonical dual of g<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font...

Fusion frames have become a major tool in the implementation of distributed systems. The effectiveness of fusion frame applications in distributed systems is reflected in the efficiency of the end fusion process. This in turn is reflected in the efficiency of the inversion of the fusion frame operator SW , which in turn is heavily dependent on the sparsity of SW . We will show that sparsity of ...

The Banach frame for a Banach space  can reconstruct each vector in  by the pre-frame operator or the reconstruction operator. The Banach Λ-frame for operator spaces was introduced by Kaushik, Vashisht and Khattar [Reconstruction Property and Frames in Banach Spaces, Palestine Journal of Mathematics, 3(1), 2014, 11-26]. In this paper we give necessary and sufficient conditions for the existen...