Annals of Functional Analysis最新文献

{"title":"Quasi-linear maps and image transformations","authors":"S. V. Butler","doi":"10.1007/s43034-025-00493-7","DOIUrl":"10.1007/s43034-025-00493-7","url":null,"abstract":"<div><p>Conic quasi-linear maps are nonlinear operators from <span>(C_0(X))</span> to a normed linear space <i>E</i> which preserve nonnegative linear combinations on positive cones generated by single functions; quasi-linear maps are linear on singly generated subalgebras. While nonlinear, for <span>(E = C_b(Y))</span> a quasi-linear map is bounded iff it is continuous. <span>(E = {mathbb {R}})</span> gives quasi-integrals, which correspond to (deficient) topological measures—nonsubadditive set functions generalizing measures. Like image measures <span>(mu circ u^{-1})</span>, (d-) image transformations move (deficient) topological measures from one space to another, generalizing <span>(u^{-1})</span>. We give criteria for a (d-) image transformation to be <span>(u^{-1})</span> for some proper continuous function. We study the interrelationships between (conic) quasi-linear maps, quasi-integrals, (deficient) topological measures and (d-) image transformations when <span>(E = C_0(Y), X, Y)</span> are locally compact. (Conic) quasi-homomorphisms behave like homomorphisms on singly generated subalgebras or cones. We show by construction that (conic) quasi-homomorphisms are in 1-1 correspondence with (d-) image transformations and with certain continuous proper functions. We give criteria for a (conic) quasi-linear map to be a (conic) quasi-homomorphism, and for the latter to be an algebra homomorphism. We show that one may approach a well-known result from Gelfand duality theory from the perspective of quasi-homomorphisms and image transformations. Any conic quasi-linear map or quasi-linear map is a composition of an algebra homomorphism with the basic quasi-linear map, and we give criteria for the latter to be linear. We study the adjoints of (d-) image transformations and (conic) quasi-linear maps; for (conic) quasi-homomorphisms they give Markov–Feller operators with nonlinear duals.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-025-00493-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the relationship among three types of Birkhoff–James orthogonality","authors":"Soumitra Daptari,&nbsp;Koki Igarashi,&nbsp;Jumpei Nakamura,&nbsp;Ryotaro Tanaka","doi":"10.1007/s43034-026-00531-y","DOIUrl":"10.1007/s43034-026-00531-y","url":null,"abstract":"<div><p>In this paper, we study three types of Birkhoff–James orthogonality in Hilbert <span>(C^*)</span>-modules, that is, the strong, quasi-strong, and original Birkhoff–James orthogonality. In general, the strong Birkhoff–James orthogonality is stronger than the quasi-strong Birkhoff–James orthogonality, and the quasi-strong Birkhoff–James orthogonality is stronger than the original Birkhoff–James orthogonality. Meanwhile, each reverse implication in this chain requires additional conditions. As the main results, we show that the strong and quasi-strong Birkhoff–James orthogonality are equivalent in a full Hilbert <span>(C^*)</span>-module if and only if the underlying <span>(C^*)</span>-algebra is commutative, and that the equivalence of the quasi-strong and original Birkhoff–James orthogonality in a full Hilbert <span>(C^*)</span>-module implies the primeness of the underlying <span>(C^*)</span>-algebra. Moreover, two examples, explaining the complexity of conditions for full Hilbert <span>(C^*)</span>-modules in which the quasi-strong and original Birkhoff–James orthogonality are equivalent, are given in the <span>(C^*)</span>-algebra settings.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-026-00531-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The multivariate Taylor measure function space and a generalization of Taylor’s theorem","authors":"Athanasios C. Micheas","doi":"10.1007/s43034-026-00507-y","DOIUrl":"10.1007/s43034-026-00507-y","url":null,"abstract":"<div><p>We propose a generalization of Taylor’s theorem to measurable, non-analytic functions that do not require differentiation. We study the consequences of the generalization, including the definition and properties of a new space of functions, which will be called the multivariate Taylor measure function space. We illustrate through examples that the proposed generalization emerges as a unifying framework that includes many concepts from mathematics as special cases. Applications of the new function space are also presented regarding solutions to linear and non-linear ordinary differential equations and partial differential equations.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-026-00507-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal recovery of functions determined by second-order differential operators","authors":"Bo Ling,&nbsp;Yi Gu","doi":"10.1007/s43034-026-00534-9","DOIUrl":"10.1007/s43034-026-00534-9","url":null,"abstract":"<div><p>We study the optimal recovery problem for isotropic functions defined by second-order differential operators using both function and gradient values. We establish an upper bound for the <i>n</i>th optimal error with an explicit constant, which is independent of the specific form of the differential operators. Furthermore, for self-adjoint operators, we obtain asymptotically exact results for the <i>n</i>th optimal error.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The lattice Schäffer constant","authors":"Michael A. Rincón-Villamizar,&nbsp;Timur Oikhberg","doi":"10.1007/s43034-026-00528-7","DOIUrl":"10.1007/s43034-026-00528-7","url":null,"abstract":"<div><p>For a Banach lattice <i>X</i>, its lattice Schäffer constant is defined by </p><div><div><span>$$begin{aligned} lambda ^+(X)=inf {max {Vert x+yVert ,Vert x-yVert },:,Vert xVert =Vert yVert =1,x,yge textbf{0}}. end{aligned}$$</span></div></div><p>In this paper, we investigate this constant, as well as the companion parameter </p><div><div><span>$$begin{aligned} beta (X)=inf {Vert xvee yVert ,:, Vert xVert =Vert yVert =1, x,yge textbf{0} hbox { and } xwedge y=textbf{0}}. end{aligned}$$</span></div></div><p>Our main results fall into two groups. (1) We link the behavior of the parameters <span>(lambda ^+)</span> and <span>(beta )</span> to the global properties of the lattice <i>X</i>. For instance, we prove that (i) if <span>(lambda ^+(X)&gt;1)</span>, then the Banach lattice <i>X</i> is a KB-space, and moreover, <i>X</i> is <i>q</i>-concave for some <span>(qin (1,infty ))</span>; (ii) <span>(lambda ^+(X)=1)</span> if and only if <i>X</i> contains lattice-almost isometric copies of <span>(ell _infty ^2)</span>; (iii) that <span>(lambda ^+(X)=2)</span> if and only if <i>X</i> is an abstract <i>L</i>-space; and (iv) if X is a Banach lattice with <i>p</i>-convexity constant 1, then <span>(lambda ^+(X)=2^{1/p})</span> if and only if <i>X</i> is an abstract <span>(L_p)</span>-space. (2) We establish inequalities relating <span>(lambda ^+(X))</span> to the characteristics of monotonicity, <span>(varepsilon _{0,m}(X))</span> and <span>(tilde{varepsilon }_{0,m}(X))</span>. Along the way, we compute <span>(lambda ^+(X))</span> and <span>(beta (X))</span> for various Banach lattices <i>X</i>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reproducing kernel functions in weighted Fock spaces","authors":"Zhangjian Hu,&nbsp;Xiaofen Lv,&nbsp;Alexander P. Schuster","doi":"10.1007/s43034-026-00533-w","DOIUrl":"10.1007/s43034-026-00533-w","url":null,"abstract":"<div><p>In this paper, we introduce a kind of weighted Fock space <span>(F^p_varphi )</span> on the complex plane <span>(mathbb {C})</span>, and obtain some estimates on the Bergman kernel function. As an application, we discuss the Bergman projection, density, and <span>(L^p_varphi )</span>-regularity of the canonical solution to <span>(overline{partial })</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fredholm theorems for integral equations in (L^p) spaces","authors":"Sheng-Ya Feng,&nbsp;Der-Chen Chang","doi":"10.1007/s43034-026-00521-0","DOIUrl":"10.1007/s43034-026-00521-0","url":null,"abstract":"<div><p>For the Fredholm integral equations of the second kind, this paper introduces the mixed norm condition for kernel functions and establishes the Fredholm theory on <span>(L^p)</span> spaces (<span>(1 leqslant p leqslant infty )</span>) by means of the degenerate kernel approximation method. The research method in this paper frees the study of Fredholm integral equations of the second kind from the limitation of Hilbert spaces and is widely applicable to other function spaces represented by <span>(L^p)</span> spaces (usually Banach spaces), which provides important theoretical support for the research on operator theory and related mathematical physics problems. Since the obtained results are independent of the specific properties of the real line, all conclusions can be directly generalized to high-dimensional Euclidean spaces, offering a reliable theoretical basis for the analysis of high-dimensional integral equations.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Commuting self-adjoint extensions of the partial differential operators on disconnected sets","authors":"Piyali Chakraborty,&nbsp;Dorin Ervin Dutkay","doi":"10.1007/s43034-026-00530-z","DOIUrl":"10.1007/s43034-026-00530-z","url":null,"abstract":"<div><p>We investigate the existence of commuting self-adjoint extensions of the partial differential operators </p><div><div><span>$$ D_j=frac{1}{2pi i}frac{partial }{partial x_j}, quad j=1,ldots ,d, $$</span></div></div><p>defined initially on <span>(C_0^infty (Omega ))</span>, where <span>(Omega subset mathbb {R}^d)</span> is an arbitrary open set, possibly disconnected and unbounded. This problem originates in a question of Segal and is closely related to Fuglede’s characterization of spectral sets through commuting self-adjoint extensions and orthogonal Fourier bases. While previous results of Fuglede and Pedersen established a complete correspondence for connected domains, the disconnected case presents new phenomena arising from interactions among distinct connected components. We extend the spectral-theoretic framework to arbitrary open sets and obtain a necessary and sufficient condition for the existence of commuting self-adjoint extensions of the operators <span>({D_j})</span>. The characterization is expressed in terms of a Radon measure, a multiplicity function, and a measurable matrix field that encode the spectral decomposition of the resulting commuting family. In contrast with the connected case, multiplicities greater than one may occur, and generalized eigenfunctions involve component-dependent coefficients attached to the exponential functions <span>(e_lambda (x)=e^{2pi ilambda cdot x})</span>. We further establish a characterization of spectral sets in terms of strongly continuous unitary representations acting as groups of local translations. For arbitrary open sets, we show that the existence of a group of local translations is equivalent to the spectrality of the domain. This extends the classical connection between spectral pairs, Fourier analysis, and translation symmetries beyond the connected setting. For open sets of finite measure with finitely many connected components, we prove that the associated spectral measure is atomic and that the joint spectrum is separated. We obtain an orthonormal basis consisting of piecewise exponential functions whose amplitudes may vary from one connected component to another. In the one-dimensional setting, where <span>(Omega )</span> is a countable union of intervals, we describe the corresponding unitary groups through a boundary transition matrix governing the propagation of translations across interval endpoints. Finally, for sets that tile <span>(mathbb {R}^d)</span> by a discrete subgroup, we characterize the associated pair measures and derive an explicit formula for the corresponding group of local translations, thereby extending a classical result of Fuglede from lattices to arbitrary discrete subgroups.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-026-00530-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Log-majorizations of Lemos–Soares type for the metric geometric and spectral geometric means","authors":"Jian Shi,&nbsp;Zhaoyu Wang,&nbsp;Cheng Wei","doi":"10.1007/s43034-026-00532-x","DOIUrl":"10.1007/s43034-026-00532-x","url":null,"abstract":"<div><p>The metric geometric and spectral geometric means are two essential concepts in the theory of matrix mean. In [15], Lemos and Soares asked whether there exists the following log-majorization relation for <span>(A, Bge 0)</span>, <span>(tin [0,1])</span>, </p><div><div><span>$$begin{aligned} s(A^t(Asharp _{t}B)B^{1-t}) {mathop prec limits _{(log )}} s(AB). end{aligned}$$</span></div></div><p>Recently, Gan and Kim prove alternative versions of above log-majorization for the metric geometric and spectral geometric means in [8]. In this paper, by several Furuta-type inequalities, we obtain several log-majorizations of Lemos–Soares type for the metric geometric mean and weak log-majorizations of Lemos–Soares type for the spectral geometric mean, which extend the recent results from Gan and Kim and other related results.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Exact Formula for the Lower Hewitt-Stromberg Measure of Self-Similar Sets and Its Continuity","authors":"Haythem Zyoudi","doi":"10.1007/s43034-026-00495-z","DOIUrl":"10.1007/s43034-026-00495-z","url":null,"abstract":"<div><p>This manuscript investigates the spherical density of the lower Hewitt–Stromberg measure in <span>(mathbb {R}^d)</span>. Also, we establish that if <span>(S=(S_1,ldots ,S_n))</span> is an iterated function system fulfilling the strong open set condition for some open set <i>U</i>, then </p><div><div><span>$$begin{aligned} mathcal {U}^alpha (K_S cap U(x,r)) le (2r)^alpha , end{aligned}$$</span></div></div><p>for every open ball <span>(U(x,r)subset U)</span> with <span>(xin K_S)</span> and <span>(r&gt;0)</span>. Employing this estimate, we derive an exact formula for the lower Hewitt–Stromberg measure of self-similar sets. As a consequence, we show that the mapping </p><div><div><span>$$begin{aligned} M_{SSC} longrightarrow mathbb {R}: S longmapsto mathcal {U}^alpha (K_S), end{aligned}$$</span></div></div><p>is continuous, where <span>(M_{SSC})</span> denotes the class of all iterated function systems fulfilling the strong separation condition.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}