scholarly journals Cohen Positive Strongly p -Summing and p -Dominated m-Homogeneous Polynomials

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Halima Hamdi ◽  
Samuel García-Hernández ◽  
Amar Belacel ◽  
Djamel Ouchenane ◽  
Sulima Ahmed Zubair
Keyword(s):  
Type Theorem ◽  
Homogeneous Polynomials

We introduce the concepts of Cohen positive strongly p -summing and positive p -dominated m-homogeneous polynomials. The version of Pietsch’s domination theorem for the first class among other results and a Bu-type theorem is proved, as well as some inclusions with other known spaces. Moreover, we present a characterization of these classes in tensor terms.

Signal analysis and weighted polynomial approximation

2006 ◽  
Vol 43 (2) ◽  
pp. 159-169
Author(s):  
Nguyen Xuan Ky
Keyword(s):  
Signal Analysis ◽  
Hermite Polynomials ◽  
Type Theorem ◽  
Hermite Functions ◽  
Bernstein Type ◽  
Time Frequency ◽  
Window Functions ◽  
Bernstein Type Theorem ◽  
Frequency Window

We present applications of Hermite polynomials in signal analysis. Among other result, we give a characterization of the so-called time-frequency window functions in terms of the Hermite--Fourier coefficients, a Bernstein-type theorem for the best approximations of window functions by Hermite-functions, time-frequency approximations. Some analogues for Hankel-transforms will also be considered.

A REMEZ-TYPE THEOREM FOR HOMOGENEOUS POLYNOMIALS

2006 ◽  
Vol 73 (03) ◽  
pp. 783-796 ◽  
Author(s):  
A. KROÓ ◽  
E. B. SAFF ◽  
M. YATTSELEV
Keyword(s):  
Type Theorem ◽  
Homogeneous Polynomials

SEMIDIRECT PRODUCTS IN ALGEBRAIC LOGIC AND SOLUTIONS OF THE QUANTUM YANG–BAXTER EQUATION

2008 ◽  
Vol 07 (04) ◽  
pp. 471-490 ◽  
Author(s):  
WOLFGANG RUMP
Keyword(s):  
Semidirect Product ◽  
Binary Operation ◽  
Algebraic Logic ◽  
Type Theorem ◽  
Combinatorial Theory ◽  
Baxter Equation ◽  
Semidirect Products ◽  
Special Classes

A semidirect product is introduced for cycloids, i.e. sets with a binary operation satisfying (x · y) · (x · z) = (y · x) · (y · z). Special classes of cycloids arise in the combinatorial theory of the quantum Yang–Baxter equation, and in algebraic logic. In the first instance, semidirect products can be used to construct new solutions of the quantum Yang–Baxter equation, while in algebraic logic, they lead to a characterization of L-algebras satisfying a general Glivenko type theorem.

scholarly journals The Fourier–Stieltjes algebra of a C*-dynamical system

2016 ◽  
Vol 27 (06) ◽  
pp. 1650050 ◽  
Author(s):  
Erik Bédos ◽  
Roberto Conti
Keyword(s):  
Dynamical System ◽  
Banach Algebra ◽  
Type Theorem ◽  
Positive Definiteness ◽  
Crossed Product ◽  
System Building ◽  
System A ◽  
Commutative Subalgebras ◽  
Definition Of

In analogy with the Fourier–Stieltjes algebra of a group, we associate to a unital discrete twisted [Formula: see text]-dynamical system a Banach algebra whose elements are coefficients of equivariant representations of the system. Building upon our previous work, we show that this Fourier–Stieltjes algebra embeds continuously in the Banach algebra of completely bounded multipliers of the (reduced or full) [Formula: see text]-crossed product of the system. We introduce a notion of positive definiteness and prove a Gelfand–Raikov type theorem allowing us to describe the Fourier–Stieltjes algebra of a system in a more intrinsic way. We also propose a definition of amenability for [Formula: see text]-dynamical systems and show that it implies regularity. After a study of some natural commutative subalgebras, we end with a characterization of the Fourier–Stieltjes algebra involving [Formula: see text]-correspondences over the (reduced or full) [Formula: see text]-crossed product.

scholarly journals A Characterization of a Local Vector Valued Bollobás Theorem

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Sheldon Dantas ◽  
Abraham Rueda Zoca
Keyword(s):  
Type Theorem ◽  
Complete Characterization ◽  
Strict Convexity ◽  
Bilinear Forms ◽  
Linear Functionals ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
Local Vector ◽  
Vector Valued

AbstractIn this paper, we are interested in giving two characterizations for the so-called property L$$_{o,o}$$ o , o , a local vector valued Bollobás type theorem. We say that (X, Y) has this property whenever given $$\varepsilon > 0$$ ε > 0 and an operador $$T: X \rightarrow Y$$ T : X → Y , there is $$\eta = \eta (\varepsilon , T)$$ η = η ( ε , T ) such that if x satisfies $$\Vert T(x)\Vert > 1 - \eta $$ ‖ T ( x ) ‖ > 1 - η , then there exists $$x_0 \in S_X$$ x 0 ∈ S X such that $$x_0 \approx x$$ x 0 ≈ x and T itself attains its norm at $$x_0$$ x 0 . This can be seen as a strong (although local) Bollobás theorem for operators. We prove that the pair (X, Y) has the L$$_{o,o}$$ o , o for compact operators if and only if so does $$(X, \mathbb {K})$$ ( X , K ) for linear functionals. This generalizes at once some results due to D. Sain and J. Talponen. Moreover, we present a complete characterization for when $$(X \widehat{\otimes }_\pi Y, \mathbb {K})$$ ( X ⊗ ^ π Y , K ) satisfies the L$$_{o,o}$$ o , o for linear functionals under strict convexity or Kadec–Klee property assumptions in one of the spaces. As a consequence, we generalize some results in the literature related to the strongly subdifferentiability of the projective tensor product and show that $$(L_p(\mu ) \times L_q(\nu ); \mathbb {K})$$ ( L p ( μ ) × L q ( ν ) ; K ) cannot satisfy the L$$_{o,o}$$ o , o for bilinear forms.

scholarly journals Coordinate-free characterization of homogeneous polynomials with isolated singularities

2011 ◽  
Vol 19 (4) ◽  
pp. 661-704 ◽  
Author(s):  
Irene Chen ◽  
Ke-Pao Lin ◽  
Stephen Yau ◽  
Huaiqing Zuo
Keyword(s):  
Homogeneous Polynomials ◽  
Isolated Singularities

THE STRENGTH OF RAMSEY’S THEOREM FOR COLORING RELATIVELY LARGE SETS

2014 ◽  
Vol 79 (01) ◽  
pp. 89-102 ◽  
Author(s):  
LORENZO CARLUCCI ◽  
KONRAD ZDANOWSKI
Keyword(s):  
Current Knowledge ◽  
Type Theorem ◽  
Complete Characterization ◽  
Infinite Subset ◽  
Point Of View ◽  
Ramsey's Theorem ◽  
Ramsey’S Theorem ◽  
Arithmetical Truth ◽  
Image Position

Abstract We characterize the effective content and the proof-theoretic strength of a Ramsey-type theorem for bi-colorings of so-called exactly large sets. An exactly large set is a set $X \subset {\bf{N}}$ such that ${\rm{card}}\left( X \right) = {\rm{min}}\left( X \right) + 1$ . The theorem we analyze is as follows. For every infinite subset M of N, for every coloring C of the exactly large subsets of M in two colors, there exists and infinite subset L of M such that C is constant on all exactly large subsets of L. This theorem is essentially due to Pudlák and Rödl and independently to Farmaki. We prove that—over RCA0 —this theorem is equivalent to closure under the ωth Turing jump (i.e., under arithmetical truth). Natural combinatorial theorems at this level of complexity are rare. In terms of Reverse Mathematics we give the first Ramsey-theoretic characterization of ${\rm{ACA}}_0^ +$ . Our results give a complete characterization of the theorem from the point of view of Computability Theory and of the Proof Theory of Arithmetic. This nicely extends the current knowledge about the strength of Ramsey’s Theorem. We also show that analogous results hold for a related principle based on the Regressive Ramsey’s Theorem. We conjecture that analogous results hold for larger ordinals.

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