We show that the Hilbert subspace of L2(G(F)?G(A)) generated by wave packets Eisenstein series built from discrete is whole space. Together with work Lapid [17], it achieves a proof spectral theorem R.P. Langlands ([16], [19]) based on J. Bernstein and E. [6] meromorphic continuation data. I use truncation compact sets as Arthur did for local trace formula in [2].

this paper proves the existence and uniqueness of quadratic mean almost periodic mild so-lutions for a class of stochastic dierential equations in a real separable hilbert space. themain technique is based upon an appropriate composition theorem combined with the banachcontraction mapping principle and an analytic semigroup of linear operators.

the northwestern part of the kerman cenozoic magmatic arc (kcma) contains many areas with porphyry copper mineralization. in this research, we used the advanced space-borne thermal emission and reflection radiometer (aster) and enhanced thematic mapper plus (etm+) images of this region to map the distribution of hydrothermally altered rocks, based on their mineral assemblages. the spectral meas...

Let K be a locally compact hypergroup. In this paper we initiate the concept of fundamental domain in locally compact hypergroups and then we introduce the Borel section mapping. In fact, a fundamental domain is a subset of a hypergroup K including a unique element from each cosets, and the Borel section mapping is a function which corresponds to any coset, the related unique element in the fun...

This paper is a proof of the Spectral Theorem; a theorem that was proven in the apprentice class but not in this manner. Because the Spectral Theorem is such a fundamental theorem in linear algebra, it is important to explore it further through an alternate proof.

The northwestern part of the Kerman Cenozoic magmatic arc (KCMA) contains many areas with porphyry copper mineralization. In this research, we used the advanced space-borne thermal emission and reflection radiometer (ASTER) and Enhanced Thematic Mapper plus (ETM+) images of this region to map the distribution of hydrothermally altered rocks, based on their mineral assemblages. The spectral meas...

Let A and B be closed operators on Banach spaces X and Y. Assume that A and B have nonempty resolvent sets and that the spectra of A and B are unbounded. Let 01 be a uniform cross norm on X @ Y. Using the Gelfand theory and resolvent algebra techniques, a spectral mapping theorem is proven for a certain class of rational functions of A and B. The class of admissable rational functions (includin...

This paper is concerned with the study of a class of closed linear operators densely defined on a Hilbert space H and called B-Fredholm operators. We characterize a B-Fredholm operator as the direct sum of a Fredholm closed operator and a bounded nilpotent operator. The notion of an index of a B-Fredholm operator is introduced and a characterization of B-Fredholm operators with index 0 is given...