The concepts of (internal, external) cubic soft sets, P-cubic (resp. R-cubic) soft subsets, R-union (resp. R-intersection, P-union, Pintersection) of cubic soft sets, and the complement of a cubic soft set are introduced, and several related properties are investigated. We apply the notion of cubic soft sets to BCK/BCI-algebras, and introduce the notion of cubic soft BCK/BCI-algebras. A charact...

Abstract. We examine the memorphic continuaiton of the cut-off resolvent Rχ(z) = χ(U(T, 0)− z)χ, χ(x) ∈ C 0 (R), where U(t, s) is the propagator related to the wave equation with non-trapping time-periodic perturbations (potential V (t, x) or a periodically moving obstacle) and T > 0 is the period. Assuming that Rχ(z) has no poles z with |z| ≥ 1, we establish a local energy decay and we obtain ...

One of the main features of analysis on post-critically finite self-similar (pcfss) sets is that it is possible to understand the behavior of the Laplacian and its inverse, the Green operator, in terms of the self-similar structure of the set. Indeed, a major step in the approach to analysis on self-similar fractals via Dirichlet forms was Kigami’s proof [8, 10] that for a self-similar Dirichle...

We consider the Stokes resolvent problem in a two-dimensional bounded Lipschitz domain $\Omega$ subject to homogeneous Dirichlet boundary conditions. prove $\mathrm{L}^p$-resolvent estimates for $p$ satisfying condition $\lvert 1 / p - 2 \rvert < 4 + \varepsilon$ some $\varepsilon > 0$. further show that operator admits property of maximal regularity and its $\mathrm{H}^{\infty}$-calculus is bo...

Resolvent analysis is a powerful tool in fluid mechanics, both for laminar and turbulent flows. Depending on application, computational cost still limiting factor. We develop parabolic method the calculation of low-frequency resolvent modes, associated with streaky structures, which can enable more than an order magnitude speed up compared to usual global calculations. The applied boundary laye...

Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multipliers theorems, we obtain necessary and sufficient conditions to guarantee existence and uniqueness of periodic solutions to the equation d dt (Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our res...

In this article we analyze the resolvent, the heat kernel and the spectral zeta function of the operator −d/dr−1/(4r) over the finite interval. The structural properties of these spectral functions depend strongly on the chosen self-adjoint extension of the operator, a choice being made necessary because of the singular potential present. Only for the Friedrichs extension standard properties ar...

where [g]j,l=1 defines a C ∞-smooth Riemannian metric and b = (b1, ..., bm) and q are, correspondingly, C∞-smooth complex-valued 1-form and function on M . σ is a C∞-smooth complex-valued function on ∂M and ∂ν stands for the normal derivative. Let Rλ be the resolvent of (1), (2) which is meromorphic for λ ∈ C (see Sect. 3 and [1]) and let Rλ(x, y) be its Schwartz kernel. A natural analog of the...

for simultaneously diagonalizable matrices A,B ∈ C . The unbounded drift term is defined by a skew-symmetric matrix S ∈ R. Differential operators of this form appear when investigating rotating waves in time-dependent reaction diffusion systems. As shown in a companion paper, one key assumption to prove resolvent estimates of L∞ in L (R,C ), 1 < p < ∞, is the following L-dissipativity condition...

We show how local estimates may be obtained for holomorphic functions of a class of linear operators on a finite-dimensional linear vector space. This is accomplished by classifying the spectrum of each operator and then estimating its resolvent on certain contours in the left half-plane. We apply these methods to prove some known theorems, and in addition we obtain new estimates for the invers...