Let L be the divergence form elliptic operator with complex bounded mea-surable coefficients, ω the positive concave function on (0,∞) of strictly critical lowertype pω ∈ (0, 1] and ρ(t) = t/ω(t) for t ∈ (0,∞). In this paper, the authorsstudy the Orlicz-Hardy spaceHω,L(R) and its dual spaceBMOρ,L∗(R), where L∗denotes the adjoint operator of L in L(R). Several characteriz...

This article investigates the soft-interior (se) and the soft-cover (sc) of operator ideals. These operations, and especially the first one, have been widely used before, but making their role explicit and analyzing their interplay with the arithmetic mean operations is essential for the study in [10] of the multiplicity of traces. Many classical ideals are “soft”, i.e., coincide with their sof...

We characterize interior transmission eigenvalues of penetrable anisotropic acoustic scattering objects by a technique known as inside-outside duality. This method has recently been identified to be able to link interior eigenvalues of the penetrable scatterer with the behavior of the eigenvalues of the far field operator for the corresponding exterior time-harmonic scattering problem. A basic ...

This paper sheds a new light on submodular function minimization and maximization from the viewpoint of discrete convex analysis. L-convex functions and M-concave functions constitute subclasses of submodular functions on an integer interval. Whereas L-convex functions can be minimized efficiently on the basis of submodular (set) function minimization algorithms, M-concave functions are identif...

We suggest a novel attentional mechanism for detection of smooth convex and concave objects based on direct processing of intensity values. The operator detects the regions of the eyes and hair in a facial image, and thus allows us to infer the face location and scale. Our operator is robust to variations in illumination, scale, and face orientation. Invariance to a large family of functions, s...

An important and perhaps interesting topic in nonlinear analysis and convex optimization concerns solving inclusions of the form 0 ∈ A(x), where A is a maximal monotone operator on a Hilbert space H. Its importance in convex optimization is evidenced from the fact that many problems that involve convexity can be formulated as finding zeros of maximal monotone operators. For example, convex mini...

This paper is devoted to description of interpolation orbits with respect to linear operators mapping an arbitrary couple of L p spaces with weights {L p 0 (U 0), L p 1 (U 1)} into an arbitrary couple {L q 0 (V 0), L q 1 (V 1)}, where 1 ≤ p 0 , p 1 , q 0 , q 1 ≤ ∞. By L p (U) we denote the space of measurable functions f on a measure space M such that f U ∈ L p with the norm f Lp(U) = f U Lp. }...

In this paper, by introducing the concept of a generalized concave operator and the properties of cone and monotone iterative technique in ordered Banach spaces, some new existence and uniqueness theorems of fixed points for the operator under more extensive conditions are obtained. Finally, as applications, we apply the results obtained in this paper to study the existence and uniqueness of po...