We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...

Random Schroedinger operators with connections to spectral properties of groups and directed polymers Marcin Kotowski Doctor of Philosophy Graduate Department of Mathematics University of Toronto 2016 This thesis studies random Schroedinger operators with connections to group theory and models from statistical physics. First, we study 1D operators obtained as perturbations of the standard adjac...

Let $X_{1},...,X_{m}$ be a family of real smooth vector fields defined in $\mathbb{R}^{n}$, $1$-homogeneous with respect to nonisotropic dilations and satisfying Hörmander's rank condition at $0$ (and therefore every point $\mathbb{R}^{n}$). The are not assumed translation invariant any Lie group structure. us consider the nonvariational evolution operator \[ \mathcal{H}:=\sum_{i,j=1}^{m}a_{i,j...

A bstract We complete the calculation of element $$ {\Gamma}_{12}^q Γ 12 q decay matrix in {B}_q-{\overline{B}}_q B − ¯ mixing, q = d , s to order α...

Let $${\mathcal {L}}=-\varDelta +V$$ be a Schrödinger operator, where the nonnegative potential V belongs to reverse Hölder class $$B_{q}$$ . By aid of subordinative formula, we estimate regularities fractional heat semigroup, $$\{e^{-t{\mathcal {L}}^{\alpha }}\}_{t>0},$$ associated with {L}}$$ As an application, obtain BMO $$^{\gamma }_{{\mathcal {L}}}$$ -boundedness maximal function, and Litt...

Abstract We construct a single smooth orthogonal projection with desired localization whose average under group action yields the decomposition of identity operator. For any full rank lattice $$\Gamma \subset \mathbb {R}^d$$ Γ ⊂ R d </mm...

The following material was created with the idea of being used for an introductory fractional calculus course. A recapitulation history is presented, as well different attempts at derivatives that existed before current definitions. Properties gamma function, beta function and Mittag-Leffler are which fundamental pieces in calculus. basic properties Riemann-Liouville Caputo their implementation...

The paper deals with nonlocal differential operators possessing a term frozen (fixed) argument appearing, in particular, modelling various physical systems feedback. presence of feedback means that the external affect on system depends its current state. If this state is taken into account only at some fixed point, then mathematically corresponds to an operator argument. In present paper, we co...