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Journal articles on the topic 'Orthogonal Complement Spaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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1

Fricain, Emmanuel, Andreas Hartmann, and William T. Ross. "Range Spaces of Co-Analytic Toeplitz Operators." Canadian Journal of Mathematics 70, no. 6 (2018): 1261–83. http://dx.doi.org/10.4153/cjm-2017-057-4.

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AbstractIn this paper we discuss the range of a co-analytic Toeplitz operator. These range spaces are closely related to de Branges–Rovnyak spaces (in some cases they are equal as sets). In order to understand its structure, we explore when the range space decomposes into the range of an associated analytic Toeplitz operator and an identifiable orthogonal complement. For certain cases, we compute this orthogonal complement in terms of the kernel of a certain Toeplitz operator on the Hardy space, where we focus on when this kernel is a model space (backward shift invariant subspace). In the spi

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2

Narita, Keiko, Noboru Endou, and Yasunari Shidama. "The Orthogonal Projection and the Riesz Representation Theorem." Formalized Mathematics 23, no. 3 (2015): 243–52. http://dx.doi.org/10.1515/forma-2015-0020.

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Abstract In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real Hilbert spaces. Furthermore, we defined the continuity and the Lipschitz the continuity of functionals on real Hilbert spaces. Referring to the article [15], we also defined some definitions on

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3

Dragomir, Silvestru Sever. "Some Bessel type additive inequalities in inner product spaces." Studia Universitatis Babes-Bolyai Matematica 66, no. 2 (2021): 381–95. http://dx.doi.org/10.24193/subbmath.2021.2.13.

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"In this paper we obtain some additive inequalities related to the cele- brated Bessel's inequality in inner product spaces. They complement the results obtained by Boas-Bellman, Bombieri, Selberg and Heilbronn, which have been applied for almost orthogonal series and in Number Theory."

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4

BHAT, B. V. RAJARAMA. "A COMPLETELY ENTANGLED SUBSPACE OF MAXIMAL DIMENSION." International Journal of Quantum Information 04, no. 02 (2006): 325–30. http://dx.doi.org/10.1142/s0219749906001797.

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Consider a tensor product [Formula: see text] of finite-dimensional Hilbert spaces with dimension [Formula: see text], 1 ≤ i ≤ k. Then the maximum dimension possible for a subspace of [Formula: see text] with no non-zero product vector is known to be d1 d2…dk - (d1 + d2 + … + dk + k - 1. We obtain an explicit example of a subspace of this kind. We determine the set of product vectors in its orthogonal complement and show that it has the minimum dimension possible for an unextendible product basis of not necessarily orthogonal product vectors.

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5

Ferreira, Milton, and Teerapong Suksumran. "Orthogonal Gyrodecompositions of Real Inner Product Gyrogroups." Symmetry 12, no. 6 (2020): 941. http://dx.doi.org/10.3390/sym12060941.

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In this article, we prove an orthogonal decomposition theorem for real inner product gyrogroups, which unify some well-known gyrogroups in the literature: Einstein, Möbius, Proper Velocity, and Chen’s gyrogroups. This leads to the study of left (right) coset partition of a real inner product gyrogroup induced from a subgyrogroup that is a finite dimensional subspace. As a result, we obtain gyroprojectors onto the subgyrogroup and its orthogonal complement. We construct also quotient spaces and prove an associated isomorphism theorem. The left (right) cosets are characterized using gyrolines (c

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6

Ferguson, Sarah H., and Richard Rochberg. "Higher order Hilbert-Schmidt Hankel forms and tensors of analytical kernels." MATHEMATICA SCANDINAVICA 96, no. 1 (2005): 117. http://dx.doi.org/10.7146/math.scand.a-14948.

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The symbols of $n^{\hbox{th}}$-order Hankel forms defined on the product of certain reproducing kernel Hilbert spaces $H(k_{i})$, $i=1,2$, in the Hilbert-Schmidt class are shown to coincide with the orthogonal complement in $H(k_{1})\otimes H(k_{2})$ of the ideal of polynomials which vanish up to order $n$ along the diagonal. For tensor products of weighted Bergman and Dirichlet type spaces (including the Hardy space) we introduce a higher order restriction map which allows us to identify the relative quotient of the $n^{\hbox{th}}$-order ideal modulo the $(n+1)^{\hbox{st}}$-order one as a dir

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7

Lee, Hyunjin, and Young Jin Suh. "Cyclic parallel hypersurfaces in complex Grassmannians of rank 2." International Journal of Mathematics 31, no. 02 (2019): 2050014. http://dx.doi.org/10.1142/s0129167x20500147.

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The object of the paper is to study cyclic parallel hypersurfaces in complex (hyperbolic) two-plane Grassmannians which have a remarkable geometric structure as Hermitian symmetric spaces of rank 2. First, we prove that if the Reeb vector field belongs to the orthogonal complement of the maximal quaternionic subbundle, then the shape operator of a cyclic parallel hypersurface in complex hyperbolic two-plane Grassmannians is Reeb parallel. By using this fact, we classify all cyclic parallel hypersurfaces in complex hyperbolic two-plane Grassmannians with non-vanishing geodesic Reeb flow. Next,

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8

Amerik, Ekaterina, and Misha Verbitsky. "Collections of Orbits of Hyperplane Type in Homogeneous Spaces, Homogeneous Dynamics, and Hyperkähler Geometry." International Mathematics Research Notices 2020, no. 1 (2018): 25–38. http://dx.doi.org/10.1093/imrn/rnx319.

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Abstract Consider the space M = O(p, q)/O(p) × O(q) of positive p-dimensional subspaces in a pseudo-Euclidean space V of signature (p, q), where p &gt; 0, q &gt; 1 and $(p,q)\neq (1,2)$, with integral structure: $V = V_{\mathbb{Z}} \otimes \mathbb{Z}$. Let Γ be an arithmetic subgroup in $G = O(V_{\mathbb{Z}})$, and $R \subset V_{\mathbb{Z}}$ a Γ-invariant set of vectors with negative square. Denote by R⊥ the set of all positive p-planes W ⊂ V such that the orthogonal complement W⊥ contains some r ∈ R. We prove that either R⊥ is dense in M or Γ acts on R with finitely many orbits. This

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9

Akritas, A. G., G. I. Malaschonok, and P. S. Vigklas. "The SVD-Fundamental Theorem of Linear Algebra." Nonlinear Analysis: Modelling and Control 11, no. 2 (2006): 123–36. http://dx.doi.org/10.15388/na.2006.11.2.14753.

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Given an m × n matrix A, with m ≥ n, the four subspaces associated with it are shown in Fig. 1 (see [1]).  Fig. 1. The row spaces and the nullspaces of A and AT; a1 through an and h1 through hm are abbreviations of the alignerframe and hangerframe vectors respectively (see [2]). The Fundamental Theorem of Linear Algebra tells us that N(A) is the orthogonal complement of R(AT). These four subspaces tell the whole story of the Linear System Ax = y. So, for example, the absence of N(AT) indicates that a solution always exists, whereas the absence of N(A) indicates that this solu

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10

Hudzik, Henryk, Yuwen Wang, and Ruli Sha. "Orthogonally complemented subspaces in Banach spaces." Nonlinear Analysis: Theory, Methods & Applications 63, no. 5-7 (2005): e1701-e1711. http://dx.doi.org/10.1016/j.na.2005.02.002.

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11

Hudzik, Henryk, Yuwen Wang, and Ruli Sha. "Orthogonally Complemented Subspaces in Banach Spaces." Numerical Functional Analysis and Optimization 29, no. 7-8 (2008): 779–90. http://dx.doi.org/10.1080/01630560802279231.

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12

Kumar, Dr Amresh, and Dr Ram Kishore Singh. "A Role of Hilbert Space in Sampled Data to Reduced Error Accumulation by Over Sampling Then the Computational and Storage Cost Increase Using Signal Processing On 2-Sphere Dimension”." International Journal of Scientific Research and Management 8, no. 05 (2020): 386–96. http://dx.doi.org/10.18535/ijsrm/v8i05.ec02.

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Hilbert Space has wide usefulness in signal processing research. It is pitched at a graduate student level, but relies only on undergraduate background material. The needs and concerns of the researchers In engineering differ from those of the pure science. It is difficult to put the finger on what distinguishes the engineering approach that we have taken. In the end, if a potential use emerges from any result, however abstract, then an engineer would tend to attach greater value to that result. This may serve to distinguish the emphasis given by a mathematician who may be interested in the pr

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13

Duffy, Joseph. "The fallacy of modern hybrid control theory that is based on “orthogonal complements” of twist and wrench spaces." Journal of Robotic Systems 7, no. 2 (1990): 139–44. http://dx.doi.org/10.1002/rob.4620070202.

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14

Favalli, Tommaso, and Augusto Smerzi. "Time Observables in a Timeless Universe." Quantum 4 (October 29, 2020): 354. http://dx.doi.org/10.22331/q-2020-10-29-354.

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Time in quantum mechanics is peculiar: it is an observable that cannot be associated to an Hermitian operator. As a consequence it is impossible to explain dynamics in an isolated system without invoking an external classical clock, a fact that becomes particularly problematic in the context of quantum gravity. An unconventional solution was pioneered by Page and Wootters (PaW) in 1983. PaW showed that dynamics can be an emergent property of the entanglement between two subsystems of a static Universe. In this work we first investigate the possibility to introduce in this framework a Hermitian

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15

Zhang, Junpeng, Yuan Cui, Lihua Deng, et al. "Closely Spaced MEG Source Localization and Functional Connectivity Analysis Using a New Prewhitening Invariance of Noise Space Algorithm." Neural Plasticity 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/4890497.

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This paper proposed a prewhitening invariance of noise space (PW-INN) as a new magnetoencephalography (MEG) source analysis method, which is particularly suitable for localizing closely spaced and highly correlated cortical sources under real MEG noise. Conventional source localization methods, such as sLORETA and beamformer, cannot distinguish closely spaced cortical sources, especially under strong intersource correlation. Our previous work proposed an invariance of noise space (INN) method to resolve closely spaced sources, but its performance is seriously degraded under correlated noise be

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16

Labuschagne, L. E. "Characterisations of partially continuous, strictly cosingular and φ- type operators". Glasgow Mathematical Journal 33, № 2 (1991): 203–12. http://dx.doi.org/10.1017/s0017089500008235.

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We will denote the dimension of a subspace M of X by dim M and the codimension of M with respect to X by codxM or simply cod M if there is no danger of confusion. The classes of infinite dimensional and closed infinite codimensional subspaces of X will be denoted by and respectively with ℱ(X) and ℱ(X) denoting the classes of finite dimensional and of finite codimensional subspaces of X respectively. For a subspace M of X we denote the injection of M into X by and the quotient map from X onto the quotient space X/M by . Where there is no danger of confusion we will write JM and QM. The injectio

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17

Ansari, Uzair, and Abdulrahman H. Bajodah. "Robust launch vehicle’s generalized dynamic inversion attitude control." Aircraft Engineering and Aerospace Technology 89, no. 6 (2017): 902–10. http://dx.doi.org/10.1108/aeat-06-2015-0149.

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Purpose To design a robust attitude control system for the ascent flight phase of satellite launch vehicles (SLVs). Design/methodology/approach The autopilot is based on generalized dynamic inversion (GDI). Dynamic constraints are prescribed in the form of differential equations that encapsulate the control objectives, and are generalized inverted using the Moore-Penrose Generalized Inverse (MPGI) based Greville formula to obtain the control law. The MPGI is modified via a dynamic scaling factor for assuring generalized inversion singularity-robust tracking control. An additional sliding mode

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18

Lin, Zhe-Yu Daniel, Zhi-Yun Li, Haifeng Yang, et al. "Probing the temperature structure of optically thick discs using polarized emission of aligned grains." Monthly Notices of the Royal Astronomical Society 493, no. 4 (2020): 4868–83. http://dx.doi.org/10.1093/mnras/staa542.

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ABSTRACT Polarized continuum emission from aligned grains in discs around young stellar objects can be used to probe the magnetic field, radiation anisotropy, or drift between dust and gas, depending on whether the non-spherical grains are aligned magnetically, radiatively, or mechanically. We show that it can also be used to probe another key disc property – the temperature gradient – along sightlines that are optically thick, independent of the grain alignment mechanism. We first illustrate the technique analytically using a simple 1D slab model, which yields an approximate formula that rela

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19

Chau, Viet T., Zdeněk P. Bažant, and Yewang Su. "Growth model for large branched three-dimensional hydraulic crack system in gas or oil shale." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374, no. 2078 (2016): 20150418. http://dx.doi.org/10.1098/rsta.2015.0418.

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Recent analysis of gas outflow histories at wellheads shows that the hydraulic crack spacing must be of the order of 0.1 m (rather than 1 m or 10 m). Consequently, the existing models, limited to one or several cracks, are unrealistic. The reality is 10 5 –10 6 almost vertical hydraulic cracks per fracking stage. Here, we study the growth of two intersecting near-orthogonal systems of parallel hydraulic cracks spaced at 0.1 m, preferably following pre-existing rock joints. One key idea is that, to model lateral cracks branching from a primary crack wall, crack pressurization, by viscous Poiseu

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20

Collier Cameron, A., E. B. Ford, S. Shahaf, et al. "Separating planetary reflex Doppler shifts from stellar variability in the wavelength domain." Monthly Notices of the Royal Astronomical Society 505, no. 2 (2021): 1699–717. http://dx.doi.org/10.1093/mnras/stab1323.

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ABSTRACT Stellar magnetic activity produces time-varying distortions in the photospheric line profiles of solar-type stars. These lead to systematic errors in high-precision radial-velocity measurements, which limit efforts to discover and measure the masses of low-mass exoplanets with orbital periods of more than a few tens of days. We present a new data-driven method for separating Doppler shifts of dynamical origin from apparent velocity variations arising from variability-induced changes in the stellar spectrum. We show that the autocorrelation function (ACF) of the cross-correlation funct

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21

Tawfeek, Sarah, Nashat Faried, and H. A. El-Sharkawy. "Orthogonality in smooth countably normed spaces." Journal of Inequalities and Applications 2021, no. 1 (2021). http://dx.doi.org/10.1186/s13660-020-02531-5.

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AbstractWe generalize the concepts of normalized duality mapping, J-orthogonality and Birkhoff orthogonality from normed spaces to smooth countably normed spaces. We give some basic properties of J-orthogonality in smooth countably normed spaces and show a relation between J-orthogonality and metric projection on smooth uniformly convex complete countably normed spaces. Moreover, we define the J-dual cone and J-orthogonal complement on a nonempty subset S of a smooth countably normed space and prove some basic results about the J-dual cone and the J-orthogonal complement of S.

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22

İlarslan, Kazım, and Emilija Nešović. "Some characterizations of osculating curves in the Euclidean spaces." Demonstratio Mathematica 41, no. 4 (2008). http://dx.doi.org/10.1515/dema-2013-0121.

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AbstractIn this paper, we give some characterization for a osculating curve in 3-dimensional Euclidean space and we define a osculating curve in the Euclidean 4-space as a curve whose position vector always lies in orthogonal complement

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23

Kider, Jehad R. "Some Properties of Fuzzy Inner Product Space." Iraqi Journal of Science, July 31, 2021, 2384–92. http://dx.doi.org/10.24996/ijs.2021.62.7.28.

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Our goal in the present paper is to introduce a new type of fuzzy inner product space. After that, to illustrate this notion, some examples are introduced. Then we prove that that every fuzzy inner product space is a fuzzy normed space. We also prove that the cross product of two fuzzy inner spaces is again a fuzzy inner product space. Next, we prove that the fuzzy inner product is a non decreasing function. Finally, if U is a fuzzy complete fuzzy inner product space and D is a fuzzy closed subspace of U, then we prove that U can be written as a direct sum of D and the fuzzy orthogonal complem

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24

Chen, Yong, and Young Joo Lee. "Sums of Dual Toeplitz Products on the Orthogonal Complements of the Fock Spaces." Integral Equations and Operator Theory 93, no. 1 (2021). http://dx.doi.org/10.1007/s00020-021-02623-x.

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