scholarly journals Differentiable functions defined in arbitrary subsets of Euclidean space

1936 ◽  
Vol 40 (2) ◽  
pp. 309-309 ◽  
Author(s):  
Hassler Whitney
Keyword(s):  
Euclidean Space ◽  
Differentiable Functions

scholarly journals On Mappings Which Commute with Convolution

1971 ◽  
Vol 12 (1) ◽  
pp. 122-128
Author(s):  
S. R. Harasymiv
Keyword(s):  
Euclidean Space ◽  
Compact Support ◽  
Strong Topology ◽  
Dimensional Euclidean Space ◽  
Schwartz Distribution ◽  
Differentiable Functions

The symbolDwill be written for the space of indefinitely differentiable functions on the n-dimensional Euclidean spaceRnwhich have compact support andDapos; will denote the space of Schwartz distribution onRn, the topological dual ofD. Except where contrary is explicitly stated, it will be assumed thatD′ is equipped with the strong topology β (D′,D) induced byD.

scholarly journals Applications of Nachbin's Theorem concerning Dense Subalgebras of Differentiable Functions

2018 ◽  
Vol 19 (3) ◽  
pp. 465
Author(s):  
Marcia Sayuri Kashimoto
Keyword(s):  
Euclidean Space ◽  
Open Subset ◽  
Differentiable Functions ◽  
Real Functions

In this paper, we give some applications of  Nachbin's Theorem  to approximation and interpolation in the the space of all k times continuously differentiable real functions on  any open subset of the  Euclidean space.

Differentiable Functions Have Sparse Graphs

1978 ◽  
Vol 4 (1) ◽  
pp. 91
Author(s):  
Laczkovich ◽  
Petruska
Keyword(s):  
Sparse Graphs ◽  
Differentiable Functions

Symplectic capacities

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Euclidean Space ◽  
Generating Functions ◽  
Weinstein Conjecture ◽  
Finite Dimensional ◽  
Hofer Metric

This chapter returns to the problems which were formulated in Chapter 1, namely the Weinstein conjecture, the nonsqueezing theorem, and symplectic rigidity. These questions are all related to the existence and properties of symplectic capacities. The chapter begins by discussing some of the consequences which follow from the existence of capacities. In particular, it establishes symplectic rigidity and discusses the relation between capacities and the Hofer metric on the group of Hamiltonian symplectomorphisms. The chapter then introduces the Hofer–Zehnder capacity, and shows that its existence gives rise to a proof of the Weinstein conjecture for hypersurfaces of Euclidean space. The last section contains a proof that the Hofer–Zehnder capacity satisfies the required axioms. This proof translates the Hofer–Zehnder variational argument into the setting of (finite-dimensional) generating functions.

ANTI-SELF-DUAL SOLUTIONS OF THE YANG-MILLS EQUATIONS IN 4n DIMENSIONS

1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Scalar Field ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Linear Equations ◽  
Dual Solutions ◽  
Gauge Fields ◽  
System Of Equations ◽  
Semisimple Lie Algebra ◽  
Yang Mills ◽  
Self Duality

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.

scholarly journals Some generalizations of the Hermite–Hadamard integral inequality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Slavko Simić ◽  
Bandar Bin-Mohsin
Keyword(s):  
Integral Inequality ◽  
Target Function ◽  
Convexity Property ◽  
Concave Functions ◽  
Differentiable Functions

AbstractIn this article we give two possible generalizations of the Hermite–Hadamard integral inequality for the class of twice differentiable functions, where the convexity property of the target function is not assumed in advance. They represent a refinement of this inequality in the case of convex/concave functions with numerous applications.

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