Spectral-Dimension Obstructions for Operators with Superlinear Counting Laws

Fuente: arXiv

Gespeichert in:

Bibliographische Detailangaben
Hauptverfasser:	Watson, Douglas F., Valentinuzzi, Tiziano
Format:	Preprint
Veröffentlicht:	2026
Schlagworte:	Spectral Theory Number Theory 35P20 (Primary) 58J35, 11M26, 47A10 (Secondary)
Online-Zugang:	Acceder al recurso
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Ähnliche Einträge

Floquet Isospectrality of the Zero Potential for Discrete Periodic Schrödinger Operators
von: Faust, Matthew, et al.
Veröffentlicht: (2024)

Rigidity of Spectral Encodings under Weyl Growth Conditions
von: Alexa, Anton
Veröffentlicht: (2025)

Pólya's conjecture for Dirichlet eigenvalues of annuli
von: Filonov, Nikolay, et al.
Veröffentlicht: (2025)

The Weyl law for the Dirichlet Laplacian
von: Contini, Alessandro Pietro
Veröffentlicht: (2025)

Exact $L^p$ growth rates of Laplace eigenfunctions on the unit disk
von: Cheng, Haoyu
Veröffentlicht: (2026)

The spectrum of the Laplacian on closed manifolds and the heat asymptotics near conical points
von: Roidos, Nikolaos
Veröffentlicht: (2023)

Pólya's conjecture for Euclidean balls
von: Filonov, Nikolay, et al.
Veröffentlicht: (2022)

Spectral Sections
von: Prokhorova, Marina
Veröffentlicht: (2020)

Generic simplicity of ellipses
von: Hillairet, Luc, et al.
Veröffentlicht: (2024)

Convex sets can have interior hot spots
von: Pont, Jaume de Dios
Veröffentlicht: (2024)

On the geometry of star domains and the spectra of Hodge-Laplace operators
von: Licht, Martin Werner
Veröffentlicht: (2024)

Stability of a Szegő-type asymptotics
von: Müller, Peter, et al.
Veröffentlicht: (2021)

Lieb-Thirring inequalities for the Dirac operator on spheres
von: Kähler, Uwe, et al.
Veröffentlicht: (2026)

Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions
von: Benhellal, Badreddine, et al.
Veröffentlicht: (2022)

Asymptotics for the magnetic Dirichlet-to-Neumann eigenvalues in general domains
von: Helffer, Bernard, et al.
Veröffentlicht: (2025)

A note on the Maxwell's eigenvalues on thin sets
von: Ferraresso, Francesco, et al.
Veröffentlicht: (2025)

Spectral gap of random covers of negatively curved noncompact surfaces
von: Moy, Julien
Veröffentlicht: (2025)

Lieb-Thirring inequalities for the shifted Coulomb Hamiltonian
von: Corso, Thiago Carvalho, et al.
Veröffentlicht: (2024)

Commutator Estimates and Quantitative Local Weyl's Law for Schrödinger Operators with Non-Smooth Potentials
von: Cárdenas, Esteban, et al.
Veröffentlicht: (2025)

Spectral invariants of integrable polygons
von: Mårdby, Gustav, et al.
Veröffentlicht: (2024)

Counting Negative Eigenvalues for the Magnetic Pauli Operator
von: Fournais, Søren, et al.
Veröffentlicht: (2023)

Hydrogen-like Schrödinger Operators at Low Energies
von: Sussman, Ethan
Veröffentlicht: (2022)

The essential self-adjointness of the wave operator on radiative spacetimes
von: Jia, Qiuye, et al.
Veröffentlicht: (2024)

The exterior Steklov problem for Euclidean domains
von: Bundrock, Lukas, et al.
Veröffentlicht: (2025)

Stability Estimates for Commutativity Properties of the Dirichlet-to-Neumann Operator
von: Speciel, Romain
Veröffentlicht: (2025)

Semiclassical eigenvalue bounds for compact homogeneous irreducible Riemannian manifolds
von: Provenzano, Luigi, et al.
Veröffentlicht: (2025)

Explicit Semiclassical Resonances from Many Delta Functions
von: Brady, Ethan J.
Veröffentlicht: (2023)

Holomorphic Witten instanton complexes on stratified pseudomanifolds with Kähler wedge metrics
von: Jayasinghe, Gayana
Veröffentlicht: (2024)

On the singularities of the spectral shift function for some tight-binding models
von: Assal, Marouane, et al.
Veröffentlicht: (2024)

Inequalities à la Pólya for the Aharonov--Bohm eigenvalues of the disk
von: Filonov, Nikolay, et al.
Veröffentlicht: (2023)

Norm-resolvent convergence for Neumann Laplacians on manifolds thinning to graphs
von: Cherednichenko, Kirill D., et al.
Veröffentlicht: (2022)

Szegő Limit Theorem for Truncated Toeplitz Operators
von: Miheisi, Nazar, et al.
Veröffentlicht: (2024)

Homogenisation for the Robin eigenvalue problem on manifolds and flexibility of optimal Schrödinger potentials
von: Lo, Chia-Chun
Veröffentlicht: (2024)

Distribution of Eigenvalues of the Kohn Laplacian on Sphere Quotients
von: Cohen, Adam, et al.
Veröffentlicht: (2025)

Families of non-tiling domains satisfying Pólya's conjecture
von: Freitas, Pedro, et al.
Veröffentlicht: (2022)

Two-sided Lieb-Thirring bounds
von: Bachmann, Sven, et al.
Veröffentlicht: (2024)

Pólya's conjecture for thin products
von: He, Xiang, et al.
Veröffentlicht: (2024)

Threshold Hierarchy for Packet-Scale Boundary Cancellation of Dirichlet Eigenfunctions
von: Alexa, Anton
Veröffentlicht: (2026)

Spectral estimates for resolvent differences of self-adjoint elliptic operators
von: Behrndt, Jussi, et al.
Veröffentlicht: (2010)

Uncertainty Principles, Spectral Localization, and Singular Schrödinger Operators on Compact Manifolds
von: Iosevich, Alex, et al.
Veröffentlicht: (2026)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
language	"de"
VUFIND_SESSION	"57902ef8b0d98f9e7179b4730896f0fa"
ui	"standard"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790847452.8344 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "57902ef8b0d98f9e7179b4730896f0fa" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"language=de; VUFIND_SESSION=57902ef8b0d98f9e7179b4730896f0fa; ui=standard"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.147"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"41195"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2604_00052/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2604_00052/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790847452.8195
REQUEST_TIME	1790847452

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler