On an integral equation with modified argument.
On an integral of fractional power operators
For a bounded and sectorial linear operator V in a Banach space, with spectrum in the open unit disc, we study the operator . We show, for example, that Ṽ is sectorial, and asymptotically of type 0. If V has single-point spectrum 0, then Ṽ is of type 0 with a single-point spectrum, and the operator I-Ṽ satisfies the Ritt resolvent condition. These results generalize an example of Lyubich, who studied the case where V is a classical Volterra operator.
On an integral operator in the space of functions with bounded variation. II.
On an integral operator in the space of functions with bounded variation
On an integral operator on the unit ball in .
On an integral representation of antisymmetric operations in Hilbert spaces. I. Bounded operations
On an integral transform by R. S. Phillips
The properties of a transformation by R.S. Phillips, which transforms an exponentially bounded C 0-semigroup of operators T(t) to a Yosida approximation depending on h, are studied. The set of exponentially bounded, continuous functions f: [0, ∞[→ E with values in a sequentially complete L c-embedded space E is closed under the transformation. It is shown that for certain complex h and k, and that , where the limit is uniform in t on compact subsets of the positive real line. If f is Hölder-continuous...
On an integral-type operator from Privalov spaces to Bloch-type spaces
Let H(B) denote the space of all holomorphic functions on the unit ball B of ℂⁿ. Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0. We study the integral-type operator , f ∈ H(B). The boundedness and compactness of from Privalov spaces to Bloch-type spaces and little Bloch-type spaces are studied
On an integral-type operator from Zygmund-type spaces to mixed-norm spaces on the unit ball.
On an inverse scattering problem for a discontinuous Sturm-Liouville equation with a spectral parameter in the boundary condition.
On an th-order infinitesimal generator and time-dependent operator differential equation with a strongly almost periodic solution.
On analytic semigroups and cosine functions in Banach spaces
If A generates a bounded cosine function on a Banach space X then the negative square root B of A generates a holomorphic semigroup, and this semigroup is the conjugate potential transform of the cosine function. This connection is studied in detail, and it is used for a characterization of cosine function generators in terms of growth conditions on the semigroup generated by B. The characterization relies on new results on the inversion of the vector-valued conjugate potential transform.
On analyticity of Ornstein-Uhlenbeck semigroups
Let be a transition semigroup of the Hilbert space-valued nonsymmetric Ornstein-Uhlenbeck process and let denote its Gaussian invariant measure. We show that the semigroup is analytic in if and only if its generator is variational. In particular, we show that the transition semigroup of a finite dimensional Ornstein-Uhlenbeck process is analytic if and only if the Wiener process is nondegenerate.
On Apery's differential operator
On applicability of the projection method to two-dimensional Toeplitz operators with measurable symbol.
On approximation by Toeplitz operators
On approximation of compact multivalued maps in topological vector spaces.
On approximation of copulas.
On asymptotic cyclicity of doubly stochastic operators
It is proved that a doubly stochastic operator P is weakly asymptotically cyclic if it almost overlaps supports. If moreover P is Frobenius-Perron or Harris then it is strongly asymptotically cyclic.
On Atkinson Operators in Locally Convex Spaces.