On banach spaces whose duals areL 1 spaces

A structure theorem for Banach spaces whose duals areL ₁ spaces, is proved. The research of the second named author has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR 66-18 through the European Office of Aerospace Research (OAR) United States Air Force.     

On extreme points inl 1

It is proved that every bounded closed and convex subset ofl ₁ is the closed convex hull of its extreme points. The research reported in this document has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR 66-18 through the European Office of Aerospace Research (OAR) United States Air Force.     

Notes on Klee’s paper “Polyhedral sections of convex bodies”

In sections 2 and 3 two methods for proving the non existence of certain universal Banach spaces, are presented. In section 4 it is proved that every infinite-dimensional conjugate Banach space has a two-dimensional subspace whose unit cell is not a polygon. The research reported in this document has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR 66-18, through the European Office of Aerospace Research (OAR) United States Air Force.     

Existence of a σ finite invariant measure for a Markov process on a locally compact space

A σ finite invariant measure is found, for a Markov process, on a locally compact space, which maps continuous functions to continuous functions. The research reported in this document has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR 66-18, through the European Office of Aerospace Research (OAR) United States Air Force.     

Problems and methods in partial differential equations

Summary Finite part and logarithmic part of some divergent integrals with applications to theCauchy problem. A Giovanni Sansone nel suo 70^mo compleanno. The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research of the Air Research and Development Command, United States Air Force, through its European Office under Contract AF 61 (056)-86.     

On the sharpness of theorems concerning zero-free regions for certain sequences of polynomials

Summary In this paper, we establish the sharpness of a theorem concerning zero-free parabolic regions for certain sequences of polynomials satisfying a three-term recurrence relation. Similarly, we establish the sharpness of a zero-free sectorial region for certain sequences of Padé approximants toe ^z .Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-74-2688Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-74-2729, and by the Energy Research and Development Administration (ERDA) under Grant E(11-1)-2075     

On complemented subspaces ofm

It is proved that an infinite dimensional subspace ofm is complemented inm if and only if it is isomorphic tom. The research reported in this document has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR 66-18, through the European Office of Aerospace Research (OAR) United States Air Force.     

On a paper of A. Feldzamen

Results of A. Feldzamen on semi-similarity of operators are proved here using matrix methods. The use of these methods yields simpler proofs, the formulations of the theorems assume a more transparent form. The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research of the Air Research and Development Command United States Air Force through its European Office.     

Real inversion and jump formulae for the Laplace transform. Part I

Generalizations of the Laplace asymptotic method are obtained and real inversion formulae of the Post-Widder type for the Laplace transform are generalized. This paper is to be a part of the first author’s Ph.D. thesis written under the direction of the second author at The Hebrew University of Jerusalem. The participation of the second author in this paper has been sponsored in part by the Air Force Office of Scientific Research OAR through the European Office, Aerospace Research, United States Air Force.     

On series in linear topological spaces

The main result is that in every complete locally-bounded linear topological space there exist series which are unconditionally yet not absolutely convergent. Relations between absolute, unconditional and metric convergence of series are studied. The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research, OAR through the European Office, Aerospace Research, United States Air Force.     

On the asymptotic behavior of spectral functions and resolvent kernels of elliptic operators

Asymptotic formulas with remainder estimates are derived for spectral functions of general elliptic operators. The estimates are based on asymptotic expansion of resolvent kernels in the complex plane. The research of the first author reported in this document has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR 66–18, through the European Office of Aerospace Research (OAR) United States Air Force. This paper is to be part of the second author’s Ph.D. thesis written under the direction of the first author at the Hebrew University of Jerusalem.     

Continuity of Bessel potentials

It is shown that certain capacities associated with potentials of functions in Lebesgue classes are non-increasing under orthogonal projection of sets. This inequality is then used to discuss continuity of traces of potentials on subspaces of possibly low dimension. The case of principal interest is the Bessel potential. This research was partially sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under AFOSR Grant No. 883-67.     

Bemerkung zu einem Satz von H. Grauert und R. Remmert

Ohne ZusammenfassungUnterstützt durch Air Force Office of Scientific Research, through the European Office, Aerospace Research, United States Air Force, OAR 62–40.     

Theorems in the additive theory of numbers

Summary This paper extends some earlier results on difference sets andB ₂ sequences bySinger, Bose, Erd?s andTuran, andChowla. This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command, under Contract No. AF 49 (638)-213. Reproduction in whole or part is permitted for any purpose of the United States Government.     

The ergodic theorem for Markov processes

Most of the material in Sections 4-5-6-8-11 has been published in [4]-[10]. We shall deal with the asymptotical behavior of the iterates of a Markov transition function. Our aim is to generalize the results about the ‘cyclic’ convergence of the iterates of a Markov matrix. Throughout the paper functional analytic methods are used and not probabilistic arguments. The report is self contained, modulo standart results from functional analysis, except for the decomposition into conservative and dissipative parts. Also we assume the existence of an invariant σ finite measure on the conservative part. This has been proved, under some restrictions, by several authors using probabilistic methods. The research reported in this document has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR 66-18, through the European Office of Aerospace Research (OAR) United States Air Force.     

Espaces de dirichlet

Sans résumé This research was partly supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under contract No. AF 18 (600)-1109. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

The treatment of nonhomogeneous Dirichlet boundary conditions by thep-version of the finite element method

Summary The paper addresses the problem of the implementation of nonhomogeneous essential Dirichlet type boundary conditions in thep-version of the finite element method.Partially supported by the Office of Naval Research under Grant N-00014-85-K-0169Research partially supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 85-0322     

On a singular differential operator

Summary Study of the properties of a singular differential operator in one independent variable. Applications to ordinary and partial differential equations. To Giovanni Sansone on his 70^th birth day. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. 49 (638)-228.     

Real inversion and jump formula for the laplace transform,part II

A generalization of the Hirschman inversion formula and a new jump formula for the Laplace transform are proved. This paper is the second part of a paper with the same name (see this Journal v., 1, 1963, pp. 85–104). The notations used here are the same as in the first part. §1–§4 belong to the first part. This paper is to be a part of the first author’s Ph. D. thesis written under the direction of the second author at the Hebrew University, Jerusalem. The participation of the second author in this paper has been sponsored in part by the Air Force Office of Scientific Research, OAR, through the European Office of Aerospace Research, United States Air Force.     

The complementary unboundedness of dual feasible solution sets in convex programming

F.E. Clark has shown that if at least one of the feasible solution sets for a pair of dual linear programming problems is nonempty then at least one of them is both nonempty and unbounded. Subsequently, M. Avriel and A.C. Williams have obtained the same result in the more general context of (prototype posynomial) geometric programming. In this paper we show that the same result is actually false in the even more general context of convex programming — unless a certain regularity condition is satisfied.We also show that the regularity condition is so weak that it is automatically satisfied in linear programming (prototype posynomial) geometric programming, quadratic programming (with either linear or quadratic constraints),l _p -regression analysis, optimal location, roadway network analysis, and chemical equilibrium analysis. Moreover, we develop an equivalent regularity condition for each of the usual formulations of duality.Research sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR-73-2516.