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On the Rockafellar theorem for Φ γ ( · , · ) -monotone multifunctions

S. Rolewicz (2006)

Studia Mathematica

Let X be an arbitrary set, and γ: X × X → ℝ any function. Let Φ be a family of real-valued functions defined on X. Let Γ : X 2 Φ be a cyclic Φ γ ( · , · ) -monotone multifunction with non-empty values. It is shown that the following generalization of the Rockafellar theorem holds. There is a function f: X → ℝ such that Γ is contained in the Φ γ ( · , · ) -subdifferential of f, Γ ( x ) Φ γ ( · , · ) f | x .

On the Schauder fixed point theorem

Lech Górniewicz, Danuta Rozpłoch-Nowakowska (1996)

Banach Center Publications

The paper contains a survey of various results concerning the Schauder Fixed Point Theorem for metric spaces both in single-valued and multi-valued cases. A number of open problems is formulated.

On the Schrödinger heat kernel in horn-shaped domains

Gabriele Grillo (2004)

Colloquium Mathematicae

We prove pointwise lower bounds for the heat kernel of Schrödinger semigroups on Euclidean domains under Dirichlet boundary conditions. The bounds take into account non-Gaussian corrections for the kernel due to the geometry of the domain. The results are applied to prove a general lower bound for the Schrödinger heat kernel in horn-shaped domains without assuming intrinsic ultracontractivity for the free heat semigroup.

On the semi-Browder spectrum

Vladimír Kordula, Vladimír Müller, Vladimir Rakočević (1997)

Studia Mathematica

An operator in a Banach space is called upper (lower) semi-Browder if it is upper (lower) semi-Fredholm and has a finite ascent (descent). We extend this notion to n-tuples of commuting operators and show that this notion defines a joint spectrum. Further we study relations between semi-Browder and (essentially) semiregular operators.

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