Convexity, boundedness, and almost periodicity for differential equations in Hilbert space.
Convolution of Nörlund methods in non-archimedean fields
Convolution of Operators and Applications.
Convolution operators in infinite dimension.
Convolution operators on spaces of holomorphic functions
A class of convolution operators on spaces of holomorphic functions related to the Hadamard multiplication theorem for power series and generalizing infinite order Euler differential operators is introduced and investigated. Emphasis is placed on questions concerning injectivity, denseness of range and surjectivity of the operators.
Convolution-dominated integral operators
For a locally compact group G we consider the algebra CD(G) of convolution-dominated operators on L²(G), where an operator A: L²(G) → L²(G) is called convolution-dominated if there exists a ∈ L¹(G) such that for all f ∈ L²(G) |Af(x)| ≤ a⋆|f|(x), for almost all x ∈ G. (1) The case of discrete groups was treated in previous publications [fgl08a, fgl08]. For non-discrete groups we investigate a subalgebra of regular convolution-dominated operators generated by product convolution operators, where the...
Copies of ’s uniformly in the spaces and
We study the presence of copies of ’s uniformly in the spaces and . By using Dvoretzky’s theorem we deduce that if is an infinite-dimensional Banach space, then contains -uniformly copies of ’s and contains -uniformly copies of ’s for all . As an application, we show that if is an infinite-dimensional Banach space then the spaces and are distinct, extending the well-known result that the spaces and are distinct.
Correct selfadjoint and positive extensions of nondensely defined minimal symmetric operators.
Correction to "Approximation with Restricted Spectra".
Corrections to the paper “The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces“
In this paper the author proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with variable exponent. As an application he proved the boundedness of certain sublinear operators on the weighted variable Lebesgue space. The proof of the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent does not contain any mistakes. But in the proof of the boundedness of certain sublinear operators on the weighted...
Corrigenda to: "Optimal domains for the kernel operator associated with Sobolev's inequality" (Studia Math. 158 (2003), 131-152)
Corrigendum on the paper Remarks on compact operators between interpolation spaces associated to polygons.
Here are given the figures of this paper, initially published with some omissions.
Corrigendum to “Commutators on ” (Studia Math. 206 (2011), 175-190)
We give a corrected proof of Theorem 2.10 in our paper “Commutators on ” [Studia Math. 206 (2011), 175-190] for the case 1 < q < p < ∞. The case when 1 = q < p < ∞ remains open. As a consequence, the Main Theorem and Corollary 2.17 in that paper are only valid for 1 < p,q < ∞.
Corrigendum to "On the spectral multiplicity of a direct sum of operators" (Colloq. Math. 104 (2006), 105-112)
Cosine families of unbounded normal operators
Cotype and (q, 1)-summing norm in a Banach space.
Cotype of operators from C(K).
Criteria for a measurable function to generate integral operators.
Criteria for weak compactness of vector-valued integration maps
Criteria are given for determining the weak compactness, or otherwise, of the integration map associated with a vector measure. For instance, the space of integrable functions of a weakly compact integration map is necessarily normable for the mean convergence topology. Results are presented which relate weak compactness of the integration map with the property of being a bicontinuous isomorphism onto its range. Finally, a detailed description is given of the compactness properties for the integration...
Criteria on boundedness of matrix operators in weighted spaces of sequences and their applications.