Local scheduler is in charge of executing tasks on the client. Localsch task information is collected in inventory and can be found at Computer - Landesk Management - Local scheduler - Scheduled Tasks in the console. From the client Localsch.exe is in the ldclient directory on the client and creates a log file localsch.exe.log. This log will show you when tasks executed in the past. To see what localsch has curretnly scheduled you can run the command line localsch.exe /Tasks |more
Hope fully this gives you visibility into the local scheduler.