Santiago Gonzalez Zerbo, Alejandra Maestripieri, Francisco Martínez Pería
Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in detail. Then, its relationship with a linearly constrained interpolation problem is analyzed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We generalize the notion of the Arov-Krein entropy functional for the case of generalized Nevanlinna functions and obtain a representation of these functionals on solutions of indefinite interpolation problems. The case of indefinite Caratheodory problem and application to Szegő limit formula for this nonclassical case are considered in greater detail.
An indefinite variant of the abstract interpolation problem is considered. Associated to this problem is a model Pontryagin space isometric operator V. All the solutions of the problem are shown to be in a one-to-one correspondence with a subset of the set of all unitary extenions U of V. These unitary extension U of V are realized as unitary colligations with the indefinite de Branges-Rovnyak space as a state space.
An abstract indefinite least squares problem with a quadratic constraint is considered. This is a quadratic programming problem with one quadratic equality constraint, where neither the objective nor the constraint are convex functions. Necessary and sufficient conditions are found for the existence of solutions.
Abstract Indefinite Problems in Riesz Spaces with Its Applications
研究希尔伯特空间\(X\)（连续嵌入巴拿赫格\(E\)）上泛函临界点存在性，通过构造格分解获空间分解，结合下降流不变集法与莫尔斯理论得抽象不定问题多临界点存在性，最后应用于椭圆边值问题。
We study real and complex interpolation of abstract Cesàro, Copson and Tandori spaces, including the description of Calderón-Lozanovski{\v ı} construction for those spaces. The results may be regarded as generalizations of interpolation for Cesàro spaces $Ces_p(I)$ in the case of real method, but they are new even for $Ces_p(I)$ in the case of complex method. Some results for more general interpolation functors are also presented. The investigations show an interesting phenomenon that there is a big difference between interpolation of Cesàro function spaces in the cases of finite and infinite …
The algebraic structure of V.P. Potapov's Fundamental Matrix Inequality (FMI) is discussed and its interpolation meaning is analyzed. Functional model spaces are involved. A general Abstract Interpolation Problem is formulated which seems to cover all the classical and recent problems in the field and the solution set of this problem is described using the Arov--Grossman formula. The extension theory of isometric operators is the proper language for treating interpolation problems of this type.
The purpose of this work is to describe an abstract theory of Hardy-Sobolev spaces on doubling Riemannian manifolds via an atomic decomposition. We study the real interpolation of these spaces with Sobolev spaces and finally give applications to Riesz inequalities.
An indefinite generalization of Nudel'man's problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides results on existence criteria for Pick-Nevanlinna and Caratheodory-Fejer interpolation, the method yealds new results on generalized interpolation in the sense of Sarason and boundary interpolation, including properties of the finite Hilbert transform relative to weights. The main theorem appeals to the Ball and Helton almost-commutant lifting theorem to provide criteria for the existence of a solu…
$2$-rotundity of some nonseparable abstract interpolation spaces
推广Argyros-Motakis构造，定义与具有无条件基的自反空间及Schreier空间相关的不可分抽象插值空间，在族复杂度假设下证明该空间具有含不可数$1$-无条件基的$2$-圆范数。
A note on Pisier's method in interpolation of abstract Hardy spaces
本文在更一般背景下提出并证明了Pisier方法的抽象版本，应用于非交换鞅变换研究。
This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H^1. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more precise result using the real interpolation theory and we clarify the use of Hardy spaces. Then with the help of the bilinear interpolation theory, we then give applications to study bilinear operators on Lebesgue spaces. These ideas permit us to study singular operators with singularities similar to those of bilinear Calderon-Zygmund operators in a far more abs…
Following ideas from the Abstract Interpolation Problem of Katsnelson et al. (Operators in spaces of functions and problems in function theory, vol 146, pp 83-69, Naukova Dumka, Keiv, 1987) for Schur class functions, we study a general metric constrained interpolation problem for functions from a vector-valued de Branges-Rovnyak space $\mathcal{H}(K_S)$ associated with an operator-valued Schur class function $S$. A description of all solutions is obtained in terms of functions from an associated de Branges-Rovnyak space satisfying only a bound on the de Branges-Rovnyak-space norm. Attention is…
An abstract Pick interpolation theorem for a family of positive semi-definite kernels on a set $X$ is formulated. The result complements those in \cite{Ag} and \cite{AMbook} and will subsequently be applied to Pick interpolation on distinguished varieties \cite{JKM}.
Global solutions of approximation problems in Krein spaces
本文研究Krein空间中不定加权最小二乘、抽象样条与平滑三类逼近问题，分析其对每点解的存在性、线性连续解算子的存在性及J-迹算子问题的可解性。
We study maximal regularity in interpolation spaces for the sum of three closed linear operators on a Banach space, and we apply the abstract results to obtain Besov and Hölder maximal regularity for complete second order Cauchy problems under natural parabolicity assumptions. We discuss applications to partial differential equations.
Maximal regularity estimates for the abstract Cauchy problems
本研究拓展Da Prato-Grisvard极大正则性理论，确定Banach空间中扇形算子相关插值空间，建立齐次与非齐次$L^1$-、加权$L^1$-极大正则性新结果，重构Kalton-Portal刻画条件，并提出非经典插值函子下$L^p$-极大正则性的新插值框架。
The research monograph gives the first systematic exposition of the elliptic (scalar and matrix) operators theory and elliptic boundary-value problems in the scales of Hilbert spaces of Hörmander of the functions/distributions of arbitrary positive or negative smoothness. The book is based on the method of interpolation with a functional parameter for the abstract and Sobolev unitary spaces. Some results are also new for the Sobolev scales. The monograph is intended for the researches, professors and PhD students.
A new approach to interpolation of compact linear operators
本文提出通过构造特殊子空间和嵌入算子来保持算子的紧性，利用反证法简化证明过程，最终得出插值理论中的关键结论。
We propose a new viewpoint on Hilbert scales extending them by means of all Hilbert spaces that are interpolation ones between spaces on the scale. We prove that this extension admits an explicit description with the help of $\mathrm{OR}$-varying functions of the operator generating the scale. We also show that this extended Hilbert scale is obtained by the quadratic interpolation (with function parameter) between the above spaces and is closed with respect to the quadratic interpolation between Hilbert spaces. We give applications of the extended Hilbert scale to interpolational inequalities,…
We prove an abstract interpolation theorem which interpolates the (r,2)-summing and (s,2)-mixing norm of a fixed operator in the image and the range space. Combined with interpolation formulas for spaces of operators we obtain as an application the original Bennett-Carl inequalities for identities acting between Minkowski spaces l_u as well as their analogues for Schatten classes S_u. Furthermore, our techniques motivate a study of Bennett-Carl inequalities within a more general setting of symmetric Banach sequence spaces and unitary ideals.
Due to the seminal works of Hochbruck and Ostermann exponential splittings are well established numerical methods utilizing operator semigroup theory for the treatment of semilinear evolution equations whose principal linear part involves a sectorial operator with angle greater than $π/2$ (meaning essentially the holomorphy of the underlying semigroup). The present paper contributes to this subject by relaxing on the sectoriality condition, but in turn requiring that the semigroup operators act consistently on an interpolation couple (or on a scale of Banach spaces). Our conditions (on the sem…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。