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Showing 1 to 20 of 22 for “"Invariant Subspace"”.
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Domain generalization for sequential data via invariant subspace recovery
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-19 without embargo terms
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Invariant Subspace Problem and Spectral Properties of Bounded Linear Operators on Banach Spaces, Banach Lattices, and Topological Vector Spaces
… locally-convex versions of some results on the Invariant Subspace Problem on Banach lattices obtained by Y. Abramovich, C Aliprantos, and O. Burkinshaw in 1993--98. For example, we show that if S and T are two commuting positive continuous operators with finite spectral radii on a locally …
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Numerical solutions of matrix equations arising in model reduction of large-scale linear -time -invariant systems
… arising from model reduction of linear-time-invariant (LTI) systems. Such systems arise in a variety of areas, especially in circuit simulation. When an integrated circuit has millions of devices, performing a full-system simulation can be infeasible due to the time required for the nonlinear …
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Structure of Invariant Subspaces for Left-Invertible Operators on Hilbert Space
… is primarily concerned with studying the invariant subspaces of left-invertible, weighted shifts, with generalizations to left-invertible operators where applicable. The two main problems that are researched can be stated together as When does a weighted shift have the one-dimensional …
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Closability of differential operators and subjordan operators
… T is the restriction of a jordan operator to an invariant subspace, and pure subjordan if no nonzero restriction of T to an invariant subspace is jordan. The main operator theoretic result of the paper is that a compact subset of the real line is the spectrum of some pure subjordan operator if …
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Recycling Bi-Lanczos Algorithms: BiCG, CGS, and BiCGSTAB
… recycling BiCG, that recycles the Krylov subspace from one pair of linear systems to the next pair. Augmented bi-Lanczos algorithm and modified two-term recurrence are developed for using the recycle space. Recycle space is built from the approximate invariant subspace corresponding to …
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Center Manifold Dynamics in Randomly Coupled Oscillators and in Cochlea
… theorem guarantees the local existence of an invariant subspace of the activity, known as a center manifold, around nonhyperbolic fixed points. A growing number of theoretical and experimental studies suggest that neural systems utilize dynamics on center manifolds to display complex, …
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Recycling Techniques for Sequences of Linear Systems and Eigenproblems
… techniques, such as recycling preconditioners or subspaces, are popular approaches for reducing computational cost. In this thesis, we introduce two novel approaches for recycling previously computed information for a subsequent system or eigenproblem, and demonstrate good results for sequences …
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Reflexivity, elementary operators and cohomology
… we show that if S is a n-dimensional subspace of B( H), then S is [ 2n ]-reflexive, where [t] denotes the largest integer that is less than or equal to t.</p><p>We obtain some lattice-theoretic conditions on a subspace lattice L which imply alg L , is strongly rank decomposable. Let S …
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Economical sampling of parametric signals
… shifts of the summands. The delays determine a subspace that contains the signals, so estimating the shifts is equivalent to subspace estimation. By contrast, conventional sampling theory yields a least-squares approximation to a signal from a fixed shift-invariant subspace of possible …
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A class of weighted Bergman spaces, reducing subspaces for multiple weighted shifts, and dilatable operators
… In Chapter 3 we will characterize the reducing subspaces of multiple weighted shifts. The reducing subspaces of the Bergman and the Dirichlet shift of multiplicity N are portrayed from this characterization. In Chapter 4 we will introduce the class of super-isometrically dilatable operators and …
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The Irreducible Representations of D2n
… the field K of complex numbers and if U is an invariant subspace of φ, then U has a complementary reducing subspace W .</p> <p>The objective of this thesis is to find all irreducible representations of the dihedral group D2n. The reason we will work with the dihedral group is because it is one …
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Near aggregation: a time and frequency domain analysis using state trajectories and transfer function residues
… equivalent to near-unobservability (roughly, an invariant subspace close to the null space of C). Here we establish a relationship between near-unobservability and modal measures of observability as suggested by Selective Modal Analysis. With this result we then obtain an upper bound on the norm …
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Beurling-Lax Representations of Shift-Invariant Spaces, Zero-Pole Data Interpolation, and Dichotomous Transfer Function Realizations: Half-Plane/Continuous-Time Versions
Given a full-range simply-invariant shift-invariant subspace <i>M</i> of the vector-valued <i>L<sup>2</sup></i> space on the unit circle, the classical Beurling-Lax-Halmos (BLH) theorem obtains a unitary operator-valued function <i>W</i> so that <i>M</i> may be represented as the image of of the …
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Non-selfadjoint operator algebras generated by unitary semigroups
… that is, to the algebra of operators that leave invariant the subspaces in the Volterra nest and its analytic counterpart. We prove that a similar result holds for the corresponding algebras acting on Lp(R), where 1 < p < ∞. It is also shown that the reflexive closures of the Fourier binests on …
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Intertwining relations, commutativity and orbits
… of linear operators on Banach spaces and the Invariant Subspace Problem. As a consequence, the research on the Theory of Hyperclicity has increased considerably. In this manuscript, we characterize the hypercyclicity of the Cesàro means of higher-order on Banach spaces. We prove some …
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On the geometry and parametrization of almost invariant subspaces and observer theory
… "On the geometry and parametrization of almost invariant subspaces and observer theory" I consider the set of almost conditioned invariant subspaces of fixed dimension for a given fixed linear finite-dimensional time-invariant observable control system in state space form. Almost conditioned …
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Methods for Analysis of Nonlinear Thermoacoustic Systems
… found from the limit cycles and Floquet modes. Invariant subspace preconditioning, higher order prediction techniques, and multiple shooting techniques are all shown to reduce the time required to generate bifurcation surfaces. Two types of shooting are compared, and two types of matrix-free …
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A Beurling Theorem for Noncommutative Hardy Spaces Associated with a Semifinite von Neumann Algebra with Various Norms
<p>We prove Beurling-type theorems for H-invariant spaces in relation to a semifinite von Neu-mann algebra M with a semifinite, faithful, normal tracial weight τ, using an extension of Arveson’s non-commutative Hardy space H-. First we prove a Beurling-Blecher-Labuschagne theorem for …
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