Displaying similar documents to “Pseudodifferential operators on non-quasianalytic classes of Beurling type”

Isomorphic properties in spaces of compact operators

Ioana Ghenciu (2023)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We introduce the definition of p -limited completely continuous operators, 1 p < . The question of whether a space of operators has the property that every p -limited subset is relative compact when the dual of the domain and the codomain have this property is studied using p -limited completely continuous evaluation operators.

The Embeddability of c₀ in Spaces of Operators

Ioana Ghenciu, Paul Lewis (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

Results of Emmanuele and Drewnowski are used to study the containment of c₀ in the space K w * ( X * , Y ) , as well as the complementation of the space K w * ( X * , Y ) of w*-w compact operators in the space L w * ( X * , Y ) of w*-w operators from X* to Y.

Elementary operators on Banach algebras and Fourier transform

Miloš Arsenović, Dragoljub Kečkić (2006)

Studia Mathematica

Similarity:

We consider elementary operators x j = 1 n a j x b j , acting on a unital Banach algebra, where a j and b j are separately commuting families of generalized scalar elements. We give an ascent estimate and a lower bound estimate for such an operator. Additionally, we give a weak variant of the Fuglede-Putnam theorem for an elementary operator with strongly commuting families a j and b j , i.e. a j = a j ' + i a j ' ' ( b j = b j ' + i b j ' ' ), where all a j ' and a j ' ' ( b j ' and b j ' ' ) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class...

Semigroups generated by certain pseudo-differential operators on the half-space 0 + n + 1

Victoria Knopova (2004)

Colloquium Mathematicae

Similarity:

The aim of the paper is two-fold. First, we investigate the ψ-Bessel potential spaces on 0 + n + 1 and study some of their properties. Secondly, we consider the fractional powers of an operator of the form - A ± = - ψ ( D x ' ) ± / ( x n + 1 ) , ( x ' , x n + 1 ) 0 + n + 1 , where ψ ( D x ' ) is an operator with real continuous negative definite symbol ψ: ℝⁿ → ℝ. We define the domain of the operator - ( - A ± ) α and prove that with this domain it generates an L p -sub-Markovian semigroup.

Duality of matrix-weighted Besov spaces

Svetlana Roudenko (2004)

Studia Mathematica

Similarity:

We determine the duals of the homogeneous matrix-weighted Besov spaces p α q ( W ) and p α q ( W ) which were previously defined in [5]. If W is a matrix A p weight, then the dual of p α q ( W ) can be identified with p ' - α q ' ( W - p ' / p ) and, similarly, [ p α q ( W ) ] * p ' - α q ' ( W - p ' / p ) . Moreover, for certain W which may not be in the A p class, the duals of p α q ( W ) and p α q ( W ) are determined and expressed in terms of the Besov spaces p ' - α q ' ( A Q - 1 ) and p ' - α q ' ( A Q - 1 ) , which we define in terms of reducing operators A Q Q associated with W. We also develop the basic theory of these reducing operator Besov spaces....

On hyponormal operators in Krein spaces

Kevin Esmeral, Osmin Ferrer, Jorge Jalk, Boris Lora Castro (2019)

Archivum Mathematicum

Similarity:

In this paper the hyponormal operators on Krein spaces are introduced. We state conditions for the hyponormality of bounded operators focusing, in particular, on those operators T for which there exists a fundamental decomposition 𝕂 = 𝕂 + 𝕂 - of the Krein space 𝕂 with 𝕂 + and 𝕂 - invariant under T .

The ideal of p-compact operators: a tensor product approach

Daniel Galicer, Silvia Lassalle, Pablo Turco (2012)

Studia Mathematica

Similarity:

We study the space of p-compact operators, p , using the theory of tensor norms and operator ideals. We prove that p is associated to / d p , the left injective associate of the Chevet-Saphar tensor norm d p (which is equal to g p ' ' ). This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that p ( E ; F ) is equal to q ( E ; F ) for a wide range of values of p and q, and show that our results...

A compactness result in thin-film micromagnetics and the optimality of the Néel wall

Radu Ignat, Felix Otto (2008)

Journal of the European Mathematical Society

Similarity:

In this paper, we study a model for the magnetization in thin ferromagnetic films. It comes as a variational problem for S 1 -valued maps m ' (the magnetization) of two variables x ' : E ε ( m ' ) = ε | ' · m ' | 2 d x ' + 1 2 | ' | - 1 / 2 ' · m ' 2 d x ' . We are interested in the behavior of minimizers as ε 0 . They are expected to be S 1 -valued maps m ' of vanishing distributional divergence ' · m ' = 0 , so that appropriate boundary conditions enforce line discontinuities. For finite ε > 0 , these line discontinuities are approximated by smooth transition layers, the so-called Néel...

On a divisibility problem

Shichun Yang, Florian Luca, Alain Togbé (2019)

Mathematica Bohemica

Similarity:

Let p 1 , p 2 , be the sequence of all primes in ascending order. Using explicit estimates from the prime number theory, we show that if k 5 , then ( p k + 1 - 1 ) ! ( 1 2 ( p k + 1 - 1 ) ) ! p k ! , which improves a previous result of the second author.

Bigraphic pairs with a realization containing a split bipartite-graph

Jian Hua Yin, Jia-Yun Li, Jin-Zhi Du, Hai-Yan Li (2019)

Czechoslovak Mathematical Journal

Similarity:

Let K s , t be the complete bipartite graph with partite sets { x 1 , ... , x s } and { y 1 , ... , y t } . A split bipartite-graph on ( s + s ' ) + ( t + t ' ) vertices, denoted by SB s + s ' , t + t ' , is the graph obtained from K s , t by adding s ' + t ' new vertices x s + 1 , ... , x s + s ' , y t + 1 , ... , y t + t ' such that each of x s + 1 , ... , x s + s ' is adjacent to each of y 1 , ... , y t and each of y t + 1 , ... , y t + t ' is adjacent to each of x 1 , ... , x s . Let A and B be nonincreasing lists of nonnegative integers, having lengths m and n , respectively. The pair ( A ; B ) is potentially SB s + s ' , t + t ' -bigraphic if there is a simple bipartite graph containing SB s + s ' , t + t ' (with s + s ' vertices x 1 , ... , x s + s ' in the part of size m ...

Compact operators whose adjoints factor through subspaces of l p

Deba P. Sinha, Anil K. Karn (2002)

Studia Mathematica

Similarity:

For p ≥ 1, a subset K of a Banach space X is said to be relatively p-compact if K n = 1 α x : α B a l l ( l p ' ) , where p’ = p/(p-1) and x l p s ( X ) . An operator T ∈ B(X,Y) is said to be p-compact if T(Ball(X)) is relatively p-compact in Y. Similarly, weak p-compactness may be defined by considering x l p w ( X ) . It is proved that T is (weakly) p-compact if and only if T* factors through a subspace of l p in a particular manner. The normed operator ideals ( K p , κ p ) of p-compact operators and ( W p , ω p ) of weakly p-compact operators, arising from these factorizations,...

On Fourier asymptotics of a generalized Cantor measure

Bérenger Akon Kpata, Ibrahim Fofana, Konin Koua (2010)

Colloquium Mathematicae

Similarity:

Let d be a positive integer and μ a generalized Cantor measure satisfying μ = j = 1 m a j μ S j - 1 , where 0 < a j < 1 , j = 1 m a j = 1 , S j = ρ R + b j with 0 < ρ < 1 and R an orthogonal transformation of d . Then ⎧1 < p ≤ 2 ⇒ ⎨ s u p r > 0 r d ( 1 / α ' - 1 / p ' ) ( J x r | μ ̂ ( y ) | p ' d y ) 1 / p ' D ρ - d / α ' , x d , ⎩ p = 2 ⇒ infr≥1 rd(1/α’-1/2) (∫J₀r|μ̂(y)|² dy)1/2 ≥ D₂ρd/α’ , where J x r = i = 1 d ( x i - r / 2 , x i + r / 2 ) , α’ is defined by ρ d / α ' = ( j = 1 m a j p ) 1 / p and the constants D₁ and D₂ depend only on d and p.

Boundedness criteria for a class of second order nonlinear differential equations with delay

Daniel O. Adams, Mathew Omonigho Omeike, Idowu A. Osinuga, Biodun S. Badmus (2023)

Mathematica Bohemica

Similarity:

We consider certain class of second order nonlinear nonautonomous delay differential equations of the form a ( t ) x ' ' + b ( t ) g ( x , x ' ) + c ( t ) h ( x ( t - r ) ) m ( x ' ) = p ( t , x , x ' ) and ( a ( t ) x ' ) ' + b ( t ) g ( x , x ' ) + c ( t ) h ( x ( t - r ) ) m ( x ' ) = p ( t , x , x ' ) , where a , b , c , g , h , m and p are real valued functions which depend at most on the arguments displayed explicitly and r is a positive constant. Different forms of the integral inequality method were used to investigate the boundedness of all solutions and their derivatives. Here, we do not require construction of the Lyapunov-Krasovski functional to establish our results....

Convolution theorems for starlike and convex functions in the unit disc

M. Anbudurai, R. Parvatham, S. Ponnusamy, V. Singh (2004)

Annales Polonici Mathematici

Similarity:

Let A denote the space of all analytic functions in the unit disc Δ with the normalization f(0) = f’(0) − 1 = 0. For β < 1, let P β = f A : R e f ' ( z ) > β , z Δ . For λ > 0, suppose that denotes any one of the following classes of functions: M 1 , λ ( 1 ) = f : R e z ( z f ' ( z ) ) ' ' > - λ , z Δ , M 1 , λ ( 2 ) = f : R e z ( z ² f ' ' ( z ) ) ' ' > - λ , z Δ , M 1 , λ ( 3 ) = f : R e 1 / 2 ( z ( z ² f ' ( z ) ) ' ' ) ' - 1 > - λ , z Δ . The main purpose of this paper is to find conditions on λ and γ so that each f ∈ is in γ or γ , γ ∈ [0,1/2]. Here γ and γ respectively denote the class of all starlike functions of order γ and the class of all convex functions of order γ. As a consequence, we obtain...

Existence of solutions for a coupled system with φ -Laplacian operators and nonlinear coupled boundary conditions

Konan Charles Etienne Goli, Assohoun Adjé (2017)

Communications in Mathematics

Similarity:

We study the existence of solutions of the system ( φ 1 ( u 1 ' ( t ) ) ) ' = f 1 ( t , u 1 ( t ) , u 2 ( t ) , u 1 ' ( t ) , u 2 ' ( t ) ) , a.e. t [ 0 , T ] , ( φ 2 ( u 2 ' ( t ) ) ) ' = f 2 ( t , u 1 ( t ) , u 2 ( t ) , u 1 ' ( t ) , u 2 ' ( t ) ) , a.e. t [ 0 , T ] , submitted to nonlinear coupled boundary conditions on [ 0 , T ] where φ 1 , φ 2 : ( - a , a ) , with 0 < a < + , are two increasing homeomorphisms such that φ 1 ( 0 ) = φ 2 ( 0 ) = 0 , and f i : [ 0 , T ] × 4 , i { 1 , 2 } are two L 1 -Carathéodory functions. Using some new conditions and Schauder fixed point Theorem, we obtain solvability result.

Kernel theorems in spaces of generalized functions

Antoine Delcroix (2010)

Banach Center Publications

Similarity:

In analogy to the classical isomorphism between ((ℝⁿ), ' ( m ) ) and ' ( m + n ) (resp. ( ( ) , ' ( m ) ) and ' ( m + n ) ), we show that a large class of moderate linear mappings acting between the space C ( ) of compactly supported generalized functions and (ℝⁿ) of generalized functions (resp. the space ( ) of Colombeau rapidly decreasing generalized functions and the space τ ( ) of temperate ones) admits generalized integral representations, with kernels belonging to specific regular subspaces of ( m + n ) (resp. τ ( m + n ) ). The main novelty is to use...

Interpolation by elementary operators

Bojan Magajna (1993)

Studia Mathematica

Similarity:

Given two n-tuples a = ( a 1 , . . . , a n ) and b = ( b 1 , . . . , b n ) of bounded linear operators on a Hilbert space the question of when there exists an elementary operator E such that E a j = b j for all j =1,...,n, is studied. The analogous question for left multiplications (instead of elementary operators) is answered in any C*-algebra A, as a consequence of the characterization of closed left A-submodules in A n .

Order bounded composition operators on the Hardy spaces and the Nevanlinna class

Nizar Jaoua (1999)

Studia Mathematica

Similarity:

We study the order boundedness of composition operators induced by holomorphic self-maps of the open unit disc D. We consider these operators first on the Hardy spaces H p 0 < p < ∞ and then on the Nevanlinna class N. Given a non-negative increasing function h on [0,∞[, a composition operator is said to be X,Lh-order bounded (we write (X,Lh)-ob) with X = H p or X = N if its composition with the map f ↦ f*, where f* denotes the radial limit of f, is order bounded from X into L h . We give...

Characterization of surjective convolution operators on Sato's hyperfunctions

Michael Langenbruch (2010)

Banach Center Publications

Similarity:

Let μ ( d ) ' be an analytic functional and let T μ be the corresponding convolution operator on Sato’s space ( d ) of hyperfunctions. We show that T μ is surjective iff T μ admits an elementary solution in ( d ) iff the Fourier transform μ̂ satisfies Kawai’s slowly decreasing condition (S). We also show that there are 0 μ ( d ) ' such that T μ is not surjective on ( d ) .

Generalized Cesàro operators on certain function spaces

Sunanda Naik (2010)

Annales Polonici Mathematici

Similarity:

Motivated by some recent results by Li and Stević, in this paper we prove that a two-parameter family of Cesàro averaging operators b , c is bounded on the Dirichlet spaces p , a . We also give a short and direct proof of boundedness of b , c on the Hardy space H p for 1 < p < ∞.

E 1 -degeneration and d ' d ' ' -lemma

Tai-Wei Chen, Chung-I Ho, Jyh-Haur Teh (2016)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

For a double complex ( A , d ' , d ' ' ) , we show that if it satisfies the d ' d ' ' -lemma and the spectral sequence { E r p , q } induced by A does not degenerate at E 0 , then it degenerates at E 1 . We apply this result to prove the degeneration at E 1 of a Hodge-de Rham spectral sequence on compact bi-generalized Hermitian manifolds that satisfy a version of d ' d ' ' -lemma.

Spaces of compact operators on C ( 2 × [ 0 , α ] ) spaces

Elói Medina Galego (2011)

Colloquium Mathematicae

Similarity:

We classify, up to isomorphism, the spaces of compact operators (E,F), where E and F are the Banach spaces of all continuous functions defined on the compact spaces 2 × [ 0 , α ] , the topological products of Cantor cubes 2 and intervals of ordinal numbers [0,α].

On the vector-valued Fourier transform and compatibility of operators

In Sook Park (2005)

Studia Mathematica

Similarity:

Let be a locally compact abelian group and let 1 < p ≤ 2. ’ is the dual group of , and p’ the conjugate exponent of p. An operator T between Banach spaces X and Y is said to be compatible with the Fourier transform F if F T : L p ( ) X L p ' ( ' ) Y admits a continuous extension [ F , T ] : [ L p ( ) , X ] [ L p ' ( ' ) , Y ] . Let T p denote the collection of such T’s. We show that T p × = T p × = T p × for any and positive integer n. Moreover, if the factor group of by its identity component is a direct sum of a torsion-free group and a finite group with discrete topology then...