# The compactness theorem

Xem 1-18 trên 18 kết quả The compactness theorem
• ### The Invariance of the Index of Elliptic Operators, elliptic operators

Abstract In 1963 Atiyah and Singer proved the famous Atiyah-Singer Index Theorem, which states, among other things, that the space of elliptic pseudodiﬀerential operators is such that the collection of operators with any given index forms a connected subset. Contained in this statement is the somewhat more specialized claim that the index of an elliptic operator must be invariant under suﬃciently small perturbations.

• ### Logic For Everyone

The discipline known as Mathematical Logic will not speciﬁcally be deﬁned within this text. Instead, you will study some of the concepts in this signiﬁcant discipline by actually doing mathematical logic. Thus, you will be able to surmise for yourself what the mathematical logician is attempting to accomplish. Consider the following three arguments taken from the disciplines of military science, biology, and set-theory, where the symbols (a), (b), (c), (d), (e) are used only to locate speciﬁc sentences....

• ### Báo cáo " On the matheron theorem for topological spaces"

In this paper we study the extending of the Matheron theorem for general topological spaces. We also show some examples about the spaces F such that the miss-and-hit topology on those spaces are unseparated or non-Hausdorff. 1. Introduction The Choquet theorem (see [1, 2]) plays very importance role in theory of random sets. The proof of this theorem is based on the Matheron theorem and especially, the locally compact property of the space F , where F is a space of all close subsets of a given space E and F is equipped with the miss-and-hit topology (see [1]). ...

• ### Đề tài " A quantitative version of the idempotent theorem in harmonic analysis "

Suppose that G is a locally compact abelian group, and write M(G) for the algebra of bounded, regular, complex-valued measures under convolution. A measure µ ∈ M(G) is said to be idempotent if µ ∗ µ = µ, or alternatively if µ takes only the values 0 and 1. The Cohen-Helson-Rudin idempotent theorem states that a measure µ is idempotent if and only if the set {γ ∈ G : µ(γ) = 1} belongs to the coset ring of G, 1. Introduction Let

• ### Korovkin type approximation theorem for functions of two variables in statistical sense

In this paper, using the concept of A-statistical convergence for double sequences, we investigate a Korovkin-type approximation theorem for sequences of positive linear operator on the space of all continuous real valued functions defined on any compact subset of the real two-dimensional space.

• ### Generalization of the Gauss–Lucas theorem for bicomplex polynomials

The aim of this paper is to extend the domain of the Gauss–Lucas theorem from the set of complex numbers to the set of bicomplex numbers. We also discuss a bicomplex version of another compact generalization of the Gauss–Lucas theorem.

• ### Automorphism Groups of (M−1)-surfaces with the M-property

A compact Riemann surface X of genus g is called an (M−1)-surface if it admits an anticonformal involution that fixes g simple closed curves, the second maximum number by Harnack’s theorem. In this paper we investigate the automorphism groups of (M−1)- surfaces with the M-property.

• ### Primary finitely compactly packed modules and S-avoidance theorem for modules

In this paper we introduce the concept of primary finitely compactly packed modules, which generalizes the concept of primary compactly packed modules. We first find the conditions that make the primary finitely compactly packed modules primary compactly packed.

• ### On the summability methods of logarithmic type and the Berezin symbol

We prove by means of the Berezin symbols some theorems for the (L)-summability method for sequences and series. Also, we prove a new Tauberian type theorem for (L)-summability.

• ### functional analysis, sobolev spaces and partial differential equations: part 1

(bq) part 1 book "functional analysis, sobolev spaces and partial differential equations" has contents: the hahn–banach theorems - introduction to the theory of conjugate convex functions; the uniform boundedness principle and the closed graph theorem; compact operators - spectral decomposition of self adjoint compact operators,...and other contents.

• ### Đề tài " Geometrization of 3dimensional orbifolds "

This paper is devoted to the proof of the orbifold theorem: If O is a compact connected orientable irreducible and topologically atoroidal 3-orbifold with nonempty ramiﬁcation locus, then O is geometric (i.e. has a metric of constant curvature or is Seifert ﬁbred). As a corollary, any smooth orientationpreserving nonfree ﬁnite group action on S 3 is conjugate to an orthogonal action. Contents 1. Introduction 2. 3-dimensional orbifolds 2.1. Basic deﬁnitions 2.2. Spherical and toric decompositions 2.3. Finite group actions on spheres with ﬁxed points 2.4.

• ### Đề tài " A Paley-Wiener theorem for reductive symmetric spaces "

Let X = G/H be a reductive symmetric space and K a maximal compact subgroup of G. The image under the Fourier transform of the space of K-ﬁnite compactly supported smooth functions on X is characterized. Contents 1. Introduction 2. Notation 3. The Paley-Wiener space. Main theorem 4. Pseudo wave packets 5. Generalized Eisenstein integrals 6. Induction of Arthur-Campoli relations 7. A property of the Arthur-Campoli relations 8. Proof of Theorem 4.4 9.

• ### Đề tài " Density of hyperbolicity in dimension one "

Annals of Mathematics In this paper we will solve one of the central problems in dynamical systems: Theorem 1 (Density of hyperbolicity for real polynomials). Any real polynomial can be approximated by hyperbolic real polynomials of the same degree. Here we say that a real polynomial is hyperbolic or Axiom A, if the real line is the union of a repelling hyperbolic set, the basin of hyperbolic attracting periodic points and the basin of inﬁnity.

• ### One-Parameter Semigroups for Linear Evolution Equations

The theory of one-parameter semigroups of linear operators on Banach spaces started in the first half of this century, acquired its core in 1948 with the Hille–Yosida generation theorem, and attained its first apex with the 1957 edition of Semigroups and Functional Analysis by E. Hille and R.S. Phillips. In the 1970s and 80s, thanks to the efforts of many different schools, the theory reached a certain state of perfection, which is well represented in the monographs by E.B. Davies [Dav80], J.A. Goldstein [Gol85], A. Pazy [Paz83], and others.

• ### Existence, uniqueness and stability solution of volterra friedholm of integro differential equations

This article investigates existence, uniqueness and stability solutions of new Volterra- Friedholm of integro-differential equations by using both method Picard approximation and Banach fixed point theorem which was introduced by Rama. Theorems on existence and uniqueness of a solution are established under some necessary and sufficient conditions on compact spaces. Also expand the some results gained by Butris.

• ### Đề tài " Invariant measures and arithmetic quantum unique ergodicity "

We classify measures on the locally homogeneous space Γ\ SL(2, R) × L which are invariant and have positive entropy under the diagonal subgroup of SL(2, R) and recurrent under L. This classiﬁcation can be used to show arithmetic quantum unique ergodicity for compact arithmetic surfaces, and a similar but slightly weaker result for the ﬁnite volume case. Other applications are also presented. In the appendix, joint with D. Rudolph, we present a maximal ergodic theorem, related to a theorem of Hurewicz, which is used in theproof of the main result. ...

• ### Đề tài " Quasi-actions on trees I. Bounded valence "

Given a bounded valence, bushy tree T , we prove that any cobounded quasi-action of a group G on T is quasiconjugate to an action of G on another bounded valence, bushy tree T . This theorem has many applications: quasi-isometric rigidity for fundamental groups of ﬁnite, bushy graphs of coarse PD(n) groups for each ﬁxed n; a generalization to actions on Cantor sets of Sullivan’s theorem about uniformly quasiconformal actions on the 2-sphere; and a characterization of locally compact topological groups which contain a virtually free group as a cocompact lattice. ...

• ### A Course in Simple-Homotopy Theory

This book grew out of courses which I taught at Cornell University and the University of Warwick during 1969 and 1970. I wrote it because of a strong belief that there should be readily available a semi-historical and geometrically motivated exposition of J. H. C. Whitehead's beautiful theory of simple-homotopy types; that the best way to understand this theory is to know how and why it was built.