Abstract: We show that the Lieb-Thirring inequalities on moments of negative eigenvalues of Schrodinger-like operators remain true, with possibly different constants, when the critical Hardy-weight C │x│^(-2) is subtracted from the Laplace operator. We do so by first establishing a Sobolev inequality for such operators. Similar results are true for fractional powers of the Laplacian and the Hardy-weight and, in particular, for relativistic Schrodinger operators. We also allow for the inclusion of magnetic vector potentials. As an application, we extend, for the first time, the proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge Zɑ = 2/π, for ɑ less than some critical value.

Abstract: Introduction Boundedness of operators on characteristic functions and the Hardy operator Lorentz spaces The Hardy-Littlewood maximal operator in weighted Lorentz spaces Bibliography Index.

Abstract: The Laplace-Poisson equation -- Distributions -- Sobolev spaces on R-n and R-n+ -- Sobolev spaces on domains -- Elliptic operators in L-2 -- Spectral theory in Hilbert spaces and Banach spaces -- Compact embeddings, spectral theory of elliptic operators -- Domains, basic spaces, and integral formulae -- Orthonormal bases of trigonometric functions -- Operator theory -- Some integral inequalities -- Function spaces.

Abstract: Hardy-Littlewood Maxial Operator Singular Integral Operators Fractional Integral Operators Oscillatory Singular Integrals Littlewood-Paley Operator.

Abstract: For every p⩾2, we obtained an explicit construction of a family of W(2,2p−1) modules, which decompose as direct sum of simple Virasoro algebra modules. Furthermore, we classified all irreducible self-dual W(2,2p−1) modules, we described their internal structure, and computed their graded dimensions. In addition, we constructed certain hidden logarithmic intertwining operators among two ordinary and one logarithmic W(2,2p−1) modules. This work, in particular, gives a mathematically precise formulation and interpretation of what physicists have been referring to as “logarithmic conformal field theory” of central charge cp,1=1−[6(p−1)2∕p], p⩾2. Our explicit construction can be easily applied for computations of correlation functions. Techniques from this paper can be used to study the triplet vertex operator algebra W(2,(2p−1)3) and other logarithmic models.

Abstract: We study classical interpolation operators for finite elements, like the Scott–Zhang operator, in the context of Orlicz–Sobolev spaces. Furthermore, we show estimates for these operators with respect to quasi-norms which appear in the study of systems of p-Laplace type.

Abstract: For a symmetric operator or relation A with infinite deficiency indices in a Hilbert space we develop an abstract framework for the description of symmetric and selfadjoint extensions A of A as restrictions of an operator or relation T which is a core of the adjoint A . This concept is applied to second order elliptic partial dierential operators on smooth bounded domains, and a class of elliptic problems with eigenvalue dependent boundary conditions is investigated.

Abstract: The theory of random Schrodinger operators is devoted to the mathematical analysis of quantum mechanical Hamiltonians modeling disordered solids Apart from its importance in physics, it is a multifaceted subject in its own right, drawing on ideas and methods from various mathematical disciplines like functional analysis, selfadjoint operators, PDE, stochastic processes and multiscale methods The present text describes in detail a quantity encoding spectral features of random operators: the integrated density of states or spectral distribution function Various approaches to the construction of the integrated density of states and the proof of its regularity properties are presented The setting is general enough to apply to random operators on Riemannian manifolds with a discrete group action References to and a discussion of other properties of the IDS are included, as are a variety of models beyond those treated in detail here

Abstract: Let H(B) denote the space of all holomorphic functions on the unit ball In this article, we investigate the following integral operators f∈ H(B), z∈ B, where g∈ H(B) and is the radial derivative of h. The operator Tg can be considered as an extension of the Cesaro operator on the unit disk. The boundedness and compactness of the operators Tg and Ig , as well as of the product of the operators between the weighted Bloch spaces are considered.

Abstract: The notion of a maximal monotone operator is crucial in optimization as it captures both the subdifferential operator of a convex, lower semicontinuous, and proper function and any (not necessarily symmetric) continuous linear positive operator. It was recently discovered that most fundamental results on maximal monotone operators allow simpler proofs utilizing Fitzpatrick functions. In this paper, we study Fitzpatrick functions of continuous linear monotone operators defined on a Hilbert space. A novel characterization of skew operators is presented. A result by Brezis and Haraux is reproved using the Fitzpatrick function. We investigate the Fitzpatrick function of the sum of two operators, and we show that a known upper bound is actually exact in finite-dimensional and more general settings. Cyclic monotonicity properties are also analyzed, and closed forms of the Fitzpatrick functions of all orders are provided for all rotators in the Euclidean plane.

Abstract: On Hormander operators and non-holonomic geometry by P. Greiner Weyl transforms and the inverse of the sub-Laplacian on the Heisenberg group by A. Dasgupta and M. W. Wong Pseudo-differential calculus on manifolds with geometric singularities by B.-W. Schulze Corner operators and applications to elliptic complexes by C.-I. Martin Ellipticity of a class of corner operators by N. Dines Pseudodifferential methods for boundary value problems by C. L. Epstein Invertibility of parabolic Pseudodifferential operators by V. Rabinovich Semilinear pseudo-differential equations and travelling waves by M. Cappiello, T. Gramchev, and L. Rodino Continuity and compactness properties of pseudo-differential operators by E. Buzano and J. Toft Trace ideals for Fourier integral operators with non-smooth symbols by F. Concetti and J. Toft Schatten-von Neumann norm inequalities for two-wavelet localization operators by V. Catana Why use the S-transform? by R. G. Stockwell Applying the S-transform to magnetic resonance imaging texture analysis by T. A. Bjarnason, S. Drabycz, D. H. Adler, J. G. Cairncross, and J. R. Mitchell Inversion formulas for two-dimensional Stockwell transforms by Y. Liu and M. W. Wong Localization of signal and image features with the TT-transform by C. R. Pinnegar Weight functions in time-frequency analysis by K. Grochenig Shannon type sampling theorems on the Heisenberg group by R. R. Radha and S. Sivananthan Rihaczek transforms and pseudo-differential operators by A. Mohammed and M. W. Wong A unified point of view on time-frequency representations and pseudo-differential operators by P. Boggiatto, G. De Donno, and A. Oliaro Blind source separation using time-frequency analysis by R. Ashino, T. Mandai, A. Morimoto, and F. Sasaki.

Abstract: In this paper, operator based nonlinear control system of an aluminum plate with a Peltier device is designed by using operator theory. A model of an aluminum plate with a Peltier device is derived. The parameters on Peltier device of model is evaluated by experiment. After that, operator based nonlinear temperature control system by using robust right coprime factorization is designed for the model. The effectiveness of the designed system is confirmed by simulation.

Abstract: Let g: B→ℂ1 be a holomorphic map of the unit ball B. We study the following integral operators The boundedness and compactness of operators T g and L g from mixed-norm spaces to the α-Bloch space ℬα and the little α-Bloch space on the unit ball are discussed in this article.

Abstract: The inverse problem of spectral analysis for a quadratic pencil of Sturm-Liouville operators on a finite interval is considered. A uniqueness theorem is proved, a solution algorithm is presented, and sufficient conditions for the solubility of the inverse problem are obtained. Bibliography: 31 titles.

Abstract: We prove that the Neumann, Dirichlet and regularity problems for divergence form elliptic equations in the half space are well posed in $L_2$ for small complex $L_\infty$ perturbations of a coefficient matrix which is either real symmetric, of block form or constant. All matrices are assumed to be independent of the transversal coordinate. We solve the Neumann, Dirichlet and regularity problems through a new boundary operator method which makes use of operators in the functional calculus of an underlaying first order Dirac type operator. We establish quadratic estimates for this Dirac operator, which implies that the associated Hardy projection operators are bounded and depend continuously on the coefficient matrix. We also prove that certain transmission problems for $k$-forms are well posed for small perturbations of block matrices.

Abstract: In this paper, we study the inverse spectral problem on a finite interval for the integro-differential operator l which is the perturbation of the Sturm-Liouville operator by the Volterra integral operator. The potential q belongs to L2[0, π] and the kernel of the integral perturbation is integrable in its domain of definition. We obtain a local solution of the inverse reconstruction problem for the potential q, given the kernel of the integral perturbation, and prove the stability of this solution. For the spectral data we take the spectra of two operators given by the expression for l and by two pairs of boundary conditions coinciding at one of the finite points.

Abstract: This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg and lattice vertex algebras. In this paper we examine logarithmic intertwining operators associated with rank one Heisenberg vertex operator algebra M(1)a, of central charge 1 − 12a2. We classify these operators in terms of depth and provide explicit constructions in all cases. Our intertwining operators resemble puncture operators appearing in quantum Liouville field theory. Furthermore, for a = 0 we focus on the vertex operator subalgebra L(1, 0) of M(1)0 and obtain logarithmic intertwining operators among indecomposable Virasoro algebra modules. In particular, we construct explicitly a family of hidden logarithmic intertwining operators, i.e., those that operate among two ordinary and one genuine logarithmic L(1, 0)-module.

Abstract: If {γk}k=0 is a sequence of real numbers and Q = {qk(x)} ∞ k=0 is a sequence of polynomials satisfying deg(qk) = k for all non-negative integers k, then we can define a linear operator TQ on the vector space of real polynomials by TQ[qk(x)] = γkqk(x) (k = 0, 1, 2, . . . ). If the linear operator TQ has the property that it maps every real polynomial having only real zeros into another polynomial having only real zeros (or, perhaps, to the identically zero function), then the corresponding sequence {γk}k=0 is called a Qmultiplier sequence. Similarly, if the linear operator TQ has the property that it does not increase the number of non-real zeros of any polynomial (which it does not map to the identically zero function), then the corresponding sequence {γk}k=0 is called a Q-complex zero decreasing sequence, or, for brevity, a Q-CZDS. Pólya and Schur completely characterized all multiplier sequences for the standard basis { x }∞ k=0 , which we will call the classical multiplier sequences. Turán, and subsequently Bleecker and Csordas, discovered classes of H-multiplier sequences, where H denotes the set of Hermite polynomials. In this dissertation, we completely characterize H-multiplier sequences and, therefore, solve an open problem stated in the literature six years ago. We show that a sequence {γk}k=0 is a non-trivial Hmultiplier sequence if and only if {γk}k=0 is a classical multiplier sequence and, either 0 ≤ γk ≤ γk+1, or 0 ≥ γk ≥ γk+1 for all integers k ≥ 0. In order to establish this result, we prove a significant generalization of a curve theorem due to Pólya.

Abstract: We prove the existence of common universal vectors for various uncountable families of universal sequence of linear operators. In particular, we give a criterion for a one-parameter family of operators on a Banach space to have a common hypercyclic vector. This criterion relies on some tools from Probability Theory and depends on the geometry of the underlying Banach space. We also study several specific examples, such as shift operators or translation-dilation operators.

Abstract: In this paper, we develop the general approach, introduced in [l], to Lax operators on algebraic curves. We observe that the space of Lax operators is closed with respect to their usual multiplication as matrix-valued functions. We construct orthogonal and symplectic analogs of Lax operators, prove that they form almost graded Lie algebras, and construct local central extensions of these Lie algebras.

Abstract: The Quantization of Edge Symbols- On Rays of Minimal Growth for Elliptic Cone Operators- Symbolic Calculus of Pseudo-differential Operators and Curvature of Manifolds- Weyl Transforms, Heat Kernels, Green Functions and Riemann Zeta Functions on Compact Lie Groups- On the Fourier Analysis of Operators on the Torus- Wave Kernels of the Twisted Laplacian- Super-exponential Decay of Solutions to Differential Equations in ?d- Gevrey Local Solvability for Degenerate Parabolic Operators of Higher Order- A New Aspect of the L p-extension Problem for Inhomogeneous Differential Equations- Continuity in Quasi-homogeneous Sobolev Spaces for Pseudo-differential Operators with Besov Symbols- Continuity and Schatten Properties for Pseudo-differential Operators on Modulation Spaces- Algebras of Pseudo-differential Operators with Discontinuous Symbols- A Class of Quadratic Time-frequency Representations Based on the Short-time Fourier Transform- A Characterization of Stockwell Spectra- Exact and Numerical Inversion of Pseudo-differential Operators and Applications to Signal Processing- On the Product of Localization Operators- Gelfand-Shilov Spaces, Pseudo-differential Operators and Localization Operators- Continuity and Schatten Properties for Toeplitz Operators on Modulation Spaces- Microlocalization within Some Classes of Fourier Hyperfunctions

Abstract: We will introduce an operation "twisting" on Hochschild complex by analogy with Drinfeld's twisting operations. By using the twisting and derived bracket construction, we will study differential graded Lie algebra structures associated with bi-graded Hochschild complex. We will show that Rota-Baxter type operators are solutions of Maurer-Cartan equations. As an application of twisting, we will give a construction of associative Nijenhuis operators.